Quick query method for shortest propagation path with high topological connectivity

Abstract

The invention discloses a quick query method for a shortest propagation path with high topological connectivity, which comprises the following steps: acquiring TCN values among biomolecules in a given gene regulation and control network, and layering biomolecule pairs according to the TCN values to generate a hierarchical structure; executing a breadth-first search strategy based on the input initial biomolecule and the target biomolecule, and obtaining a shortest propagation path meeting TCN hierarchy constraints; searching hierarchies from top to bottom based on a hierarchical threshold list in the hierarchical structure to obtain a shortest path; and obtaining the shortest path with high topological connectivity. According to the method, the topological connectivity index TCN is defined, and measurement of the propagation potential between biological molecules in the gene regulation and control network is achieved. Different from existing research, the method needs to consider the path length and the topological connectivity index at the same time so as to guarantee the propagation speed and the relative stability of propagation at the same time.

Description

Technical Field

[0001] This application belongs to the field of computer network technology, specifically relating to a fast query method for the shortest propagation path with high topological connectivity. Background Technology

[0002] A gene regulatory network is a complex network composed of gene regulatory relationships. The propagation pathway in a gene regulatory network refers to the cascade imbalance of downstream biomolecules caused by a mutation in a biomolecule (a collective term for all nodes in the gene regulatory network) through direct or indirect regulatory relationships within the network. For example, in cancer, the mutated biomolecule TP53 exacerbates instability between molecules and uncontrolled cell proliferation through the pathway TP53→BRCA1→MYC. This pathway reveals a multi-level carcinogenic mechanism in which tumor suppressor genes trigger proto-oncogene activation through cascade regulation. In the field of computer science, the definition of a gene regulatory network emphasizes computability and predictability, rather than simply describing biological mechanisms. In computer science, a gene regulatory network is usually defined as a system that abstracts and simulates the regulatory relationships between biomolecules through computational models and algorithms. Its core objective is to use computer technology to analyze the complex logic of expression regulation, simulate interactions between biomolecules, and guide biological experimental verification.

[0003] Current research in the field of computer science focuses solely on predicting direct regulatory relationships between biomolecules, neglecting the search and prediction of indirect regulatory pathways. Furthermore, existing gene regulatory network path search problems only pursue the shortest path (based on edge weights or hop count), resulting in a rather singular objective. Summary of the Invention

[0004] This application provides a fast query method for shortest propagation paths with high topological connectivity to solve the technical problem of existing gene regulatory network path search problems that only pursue the shortest path.

[0005] To address the aforementioned technical problems, this application adopts the following technical solution: a fast query method for shortest propagation paths with high topological connectivity, comprising:

[0006] S1. Obtain the TCN values ​​between biomolecules in a given gene regulatory network, and stratify the biomolecule pairs according to their TCN values ​​to generate a hierarchical structure;

[0007] S2. Based on the input starting biomolecule and target biomolecule, execute a breadth-first search strategy to obtain the shortest path that satisfies the TCN level constraints in each level;

[0008] S3. Based on the list of hierarchical thresholds in the hierarchical structure, search the hierarchy from top to bottom to obtain the shortest path in all levels;

[0009] S4. Based on the shortest path, obtain the high topological connectivity of the shortest path.

[0010] Furthermore, the method in step S1 includes:

[0011] S11. Initialize the dictionary structure to store the TCN value of each edge;

[0012] S12. Obtain the TCN value of each edge in the gene regulation network, and store the TCN values ​​in a dictionary structure after precision processing;

[0013] S13. Based on the dictionary structure, obtain the neighbor set of the biomolecules at both ends of the edge;

[0014] S14. Sort the TCN values ​​from largest to smallest and extract all different TCN values;

[0015] S15. Generate a hierarchical structure based on the threshold list and different TCN values.

[0016] Furthermore, the method in step S2 includes:

[0017] S21. Input validity check: Verify whether the starting biomolecule belongs to the corresponding level to ensure the feasibility of subsequent searches;

[0018] S22. Initialize the queue and path record dictionary to provide data structure support for subsequent breadth-first search;

[0019] S23. Based on breadth-first search, the search is carried out layer by layer until the target biomolecule is found by traversing the neighbors of the current biomolecule, registering unvisited biomolecules and updating the queue.

[0020] S24. If the current biomolecule is equal to the target biomolecule, reconstruct the path in reverse; by backtracking the path and recording the predecessor relationships in the dictionary, generate a complete path from the target biomolecule to the starting biomolecule;

[0021] S25. Verify the validity of the path by checking whether the target biomolecule in the path is the starting biomolecule to ensure that the generated path is correct and complete.

[0022] Furthermore, the method in step S23 includes:

[0023] S231. Extract the current biomolecule and determine the termination condition;

[0024] S232. Traverse the neighbors of the current biomolecule at a given level;

[0025] S233. For each neighboring biomolecule of the current biomolecule, if it is not recorded in the path record dictionary, update the predecessor relationship and update the queue;

[0026] S234. Repeat the above steps to process the biomolecules in the queue in turn until the target biomolecule is removed.

[0027] Furthermore, the method in step S3 includes:

[0028] S31. Based on the hierarchical threshold, process the levels one by one in descending order;

[0029] S32. Search for the shortest path in the current level;

[0030] S33. Confirm the optimal path and terminate the search;

[0031] S34. If no path is found at any level, return null.

[0032] Furthermore, the method in step S32 includes:

[0033] S321. Based on the breadth-first search strategy, set the specified level as the current processing level and search for the shortest path of the current processing level;

[0034] S322. If the shortest path is found at the current level, return the shortest path as the query result. The topological connectivity of the shortest path is the threshold of the current level.

[0035] S323. If the shortest path is not found at the current level, continue processing the next lower TCN level.

[0036] The beneficial effects of this application are as follows: This application defines the topology common neighbor (TCN), which enables the measurement of the propagation potential between biomolecules in gene regulatory networks. Unlike existing studies, which require simultaneous consideration of path length and topology common neighbor to ensure both propagation speed and relative stability, this application reveals the crucial role of potential propagation pathways in driving disease cascade effects and provides a network-based perspective for predicting potential therapeutic targets. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating an embodiment of the fast query method for the shortest propagation path with high topological connectivity in this application;

[0038] Figure 2 This is a schematic diagram of a gene regulatory network, representing an embodiment of the fast query method for the shortest propagation path with high topological connectivity in this application.

[0039] Figure 3 This is a storage structure diagram of a hierarchical dictionary of an embodiment of the fast query method for the shortest propagation path with high topological connectivity in this application;

[0040] Figure 4 This is a detailed layered diagram of an embodiment of the fast query method for the shortest propagation path with high topological connectivity in this application. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments.

[0042] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0043] In this application, G=(U,E) is used to represent a gene regulatory network, where U represents the set of biomolecules in the network, and E is the set of edges connecting biomolecules, representing the regulatory relationships between biomolecules. An edge is a pair of biomolecules, denoted as (x, y). If two biomolecules have an edge between them, they can be considered neighbors.

[0044] In this application, a topological connectivity index, termed TCN (Topology Common Neighbor), is used to measure the likelihood of inter-biomolecule propagation within a gene regulatory network. Common neighbors among biomolecules in a gene regulatory network act as "bridges" for propagation pathways, significantly enhancing the probability of propagation. Biomolecule pairs with a large number of common neighbors often form multiple indirect regulatory pathways by sharing upstream regulators or downstream target genes. However, in a gene regulatory network, if common neighbors provide redundant regulatory pathways (such as multiple transcription factors activating the same gene), propagation may be buffered, making it less likely to spread. For example, genes A and B are both regulated by C and D; if C mutates, D can still maintain gene expression, reducing the risk of propagation. Therefore, TCN is obtained by normalizing the number of common neighbors using the minimum number of neighbors. Its formula is: TCN = |N(x)∩N(y)| / min(|N(x)|,|N(y)|). Here, x and y are two biomolecules that are neighbors. N(x) and N(y) are the sets of neighbors of the molecules.

[0045] If a path (u,x1,x2,...,xj,v) exists between two biomolecules u and v in a gene regulatory network, and k1,k2,k3,...,kj+1 represents the path topological connectivity of adjacent biomolecule pairs (u,x1)(x1,x2),(x2,x3),...,(xj-1,xj),(xj,v) in the path, then in the TCN value {k1,k2,k3,...,kj+1} among all adjacent biomolecules on the path, this invention uses min{k1,k2,k3,...,kj+1} to represent the path topological connectivity between u and v, denoted as pathTCN.

[0046] Given a gene regulatory network graph G=(U,E), the user-inputted starting biomolecule u represents a known pathogenic mutant gene, signifying the molecular source of disease occurrence, while the target biomolecule v represents a disease phenotype-related gene, representing the functional effector molecule at the disease endpoint. The method described in this invention searches for the propagation path with the maximum topological connectivity and the shortest path length between u and v based on the user-inputted u and v. This invention aims to reveal the crucial role of such paths in driving disease cascade effects and to provide a network-based prediction for identifying potential therapeutic targets to guide biological experimental validation.

[0047] See Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the fast query method for the shortest propagation path with high topological connectivity according to this application. The method includes:

[0048] S1. Obtain the TCN values ​​between biomolecules in a given gene regulatory network, and stratify the biomolecule pairs according to their TCN values ​​to generate a hierarchical structure.

[0049] For details, please refer to Figure 2 The method of step S1 includes:

[0050] S11. Initialize the dictionary structure to store the TCN value of each edge.

[0051] For details, please refer to Figure 2 Create an empty dictionary TCN_dict, where the keys are biomolecule pairs, such as (TP53, BRCA1), and the values ​​are their TCN values. The dictionary is initially empty and will subsequently store the calculated TCN values ​​of all edges.

[0052] S12. Obtain the TCN value of each edge in the gene regulatory network, and store the TCN values ​​in the TCN dictionary after precision processing.

[0053] Specifically, the method in step S12 includes:

[0054] S121. Taking the biomolecule pair (TP53, BRCA1) as an example, obtain the neighbor set N(TP53)={BRCA1, FANCD2, MDM2} of biomolecule TP53, with the number of neighbors |N(TP53)|=3; obtain the neighbor set N(BRCA1)={TP53, FANCD2, MYC, ATM, CHEK2} of biomolecule BRCA1, with the number of neighbors |N(y)|=5. Calculate the number of common neighbors of the two biomolecules |N|=|N(x)∩N(y)|=2 (common neighbors are BRCA1, FANCD2).

[0055] S122. Calculate the smaller value of the number of neighbors between two biomolecules: min_degree = min(3,5) = 3.

[0056] S123. Calculate the TCN value: TCN = |N| / min_degree = 2 / 3 ≈ 0.666666.

[0057] S124. Perform truncation on the TCN value to retain one decimal place (0.666666→0.6).

[0058] S125. Store the processed TCN value into the dictionary TCN_dict[(TP53, BRCA1)]=0.6.

[0059] S126. Repeat steps S121 to S125 until the TCN values ​​of all edges in the network have been calculated and stored.

[0060] S13. Based on the dictionary structure, obtain the neighbor sets of the biomolecules at both ends of the edge.

[0061] Specifically, the TCN values ​​are sorted from largest to smallest, and all distinct TCN values ​​are extracted to generate a tiered threshold list. In this example, all TCN values ​​are {0.8, 0.6, 0.5, 0.3, 0.2}. The thresholds are then sorted in descending order to generate a threshold list: thresholds_list = [0.8, 0.6, 0.5, 0.3, 0.2].

[0062] S14. Sort the TCN values ​​from largest to smallest and extract all different TCN values.

[0063] For details, please refer to Figure 3 ,like Figure 3 The hierarchical dictionary `layer_dict` is initialized as the storage structure, where the keys are the hierarchical thresholds (e.g., 0.8) and the values ​​are the set of edges that satisfy TCN ≥ the threshold. Iterate through `thresholds_list`, and for each threshold (e.g., 0.6), filter all biomolecule pairs in `TCN_dict` whose TCN value is greater than or equal to that threshold.

[0064] For example, edges in TCN_dict that satisfy TCN≥0.6 include (TP53,BRCA1), (BRCA1,FANCD2), etc. These edges are stored in layer_dict[0.6] to form the subgraph structure corresponding to the current layer.

[0065] S15. Generate a hierarchical structure based on the threshold list and different TCN values.

[0066] Specifically, it returns the layered results and generates a layered structure, including a layer dictionary layer_dict, a layer threshold list thresholds_list, and a TCN dictionary TCN_dict.

[0067] S2. Based on the input starting biomolecule and target biomolecule, execute a breadth-first search strategy to obtain the shortest path that satisfies the TCN level constraints in each level.

[0068] Specifically, based on the user-input starting biomolecule TP53 and target biomolecule MYC, a breadth-first search strategy is executed at a given level in the hierarchical dictionary structure (layer_dict) to find the shortest propagation path that satisfies the hierarchical constraints.

[0069] Among them, see Figure 4 The method of step S2 includes:

[0070] S21. Input validity check: Verify whether the starting biomolecule belongs to the corresponding level to ensure the feasibility of subsequent searches.

[0071] Specifically, check if a biomolecule pair containing TP53 and MYC exists in layer_dict[current_layer] corresponding to the current layer (e.g., current_layer=0.6). The specific method is as follows: traverse all edges in layer_dict[0.6], checking if TP53 appears in the left or right position of any edge, and simultaneously checking if MYC appears in the left or right position of any edge. If they exist, TP53 and MYC are considered to belong to the current layer; if they do not exist, skip the subsequent steps and process the next layer.

[0072] S22. Initialize the queue and path record dictionary.

[0073] Specifically, the queue and path record dictionary are initialized to provide data structure support for breadth-first search. The queue `frontier` is initialized, using a first-in, first-out (FIFO) structure, initially containing only the starting biomolecule TP53, i.e., `frontier = [TP53]`. The path record dictionary `trail` is initialized to store the precursor biomolecules for each biomolecule.

[0074] S23. Based on breadth-first search, the search is carried out layer by layer until the target biomolecule is found by traversing the neighbors of the current biomolecule, registering unvisited biomolecules and updating the queue.

[0075] Specifically, the method in step S23 includes:

[0076] S231. Extract the current biomolecule and determine the termination condition.

[0077] Specifically, the current biomolecule (initially TP53) is retrieved from the front of the queue and its identity is determined. If it is not the target biomolecule MYC, the search continues.

[0078] S232. Traverse the neighbors of the current biomolecule at a given level.

[0079] Specifically, iterate through all neighbors of the current biomolecule in the current_layer (e.g., 0.6). Based on layer_dict[current_layer], obtain the neighbor set of TP53 (e.g., BRCA1).

[0080] S233. For each neighboring biomolecule of the current biomolecule, if it is not recorded in the path record dictionary, update the predecessor relationship and update the queue.

[0081] Specifically, register unvisited neighbor biomolecules. For each neighbor (e.g., BRCA1), if the neighbor is not recorded in the trail (i.e., has not been visited), update trail[BRCA1] = TP53, indicating that the predecessor of BRCA1 is TP53. Add the neighbor to the end of the queue and update the queue to frontier = [BRCA1].

[0082] S234. Repeat the above steps to process the biomolecules in the queue sequentially until the target biomolecule is removed.

[0083] Specifically, repeat steps S231 to S233 to process the biomolecules in the queue sequentially until the target biomolecule MYC is removed from the queue, at which point the search loop terminates.

[0084] S24. If the current biomolecule is equal to the target biomolecule V, reconstruct the path in reverse; by backtracking the path and recording the predecessor relationships in the dictionary, generate a complete path from the target biomolecule to the starting biomolecule.

[0085] Specifically, the method in step S24 includes:

[0086] S241. Initialize the path shortest_path.

[0087] Specifically, the path is constructed starting from the target biomolecule v. The initial path is a list containing only v (shortest_path=[v]), and it needs to be traced back to the starting point u.

[0088] For example, the initial path shortest_path is backtracked from the target MYC, with the initial path being [MYC].

[0089] S24. Tracing back to precursor biomolecules.

[0090] Specifically, the path record dictionary (trail) is accessed iteratively, and the predecessor of the first biomolecule in the current path is inserted at the beginning of the path. For example, if trail[v] = x, the path is updated to [x, v]; if trail[x] = u, the path is further updated to [u, x, v]. This process continues until the path backtracks to the starting biomolecule u, i.e., trail[u] = None, forming the complete path shortest_path.

[0091] For example, the trail dictionary is used to backtrack the precursor biomolecule level by level: trail[MYC] = FANCD2, the path is updated to [FANCD2, MYC]. trail[FANCD2] = BRCA1, the path is updated to [BRCA1, FANCD2, MYC]. trail[BRCA1] = TP53, the path is updated to [TP53, BRCA1, FANCD2, MYC]. Backtracking terminates when the starting biomolecule TP53 is reached (i.e., trail[TP53] = None).

[0092] S25. Verify the validity of the path by checking whether the target biomolecule in the path is the starting biomolecule to ensure that the generated path is correct and complete.

[0093] Specifically, check the first biomolecule of the path. If the first biomolecule of the path is u (e.g., shortest_path = [u,x,v]), then the path is considered valid and the result is returned. If the first biomolecule is not u (e.g., the path is shortest_path = [x,v]), it means that there is no path between the starting biomolecule and the target biomolecule at the target level, and a null value is returned.

[0094] S3. Based on the thresholds list in the hierarchical structure, search the hierarchy from top to bottom to obtain the shortest path in all levels.

[0095] Specifically, the method in step S3 includes:

[0096] S31. Based on the hierarchical threshold, process each level in descending order.

[0097] Specifically, the highest unprocessed level threshold is selected from the pre-generated thresholds list as the constraint for the current level, ensuring that paths are searched first in the high TCN threshold level.

[0098] S32. Search for the shortest path in the current level.

[0099] Specifically, the method in step S32 includes:

[0100] S321. Based on the breadth-first search strategy, set the specified level as the current level and search for the shortest path of the current level.

[0101] Specifically, the method of searching for the shortest path at a specified level in step S2 is used, and the specified level is set as the currently processed level (current_layer). For example, if the threshold of the currently processed level is 0.6, i.e., current_layer=0.6, this step only searches for paths in the level dictionary layer_dict[0.6]. This step attempts to find the shortest path from the starting biomolecule to the target biomolecule in the current level.

[0102] S322. If the shortest path is found at the current level, return the shortest path as the query result. The topological connectivity of the shortest path is the threshold of the current level.

[0103] Specifically, if the shortest path (shortest_path) is found at the current level, the path is returned as the query result for this step, and the topological connectivity of the path is the threshold of the current level (i.e., pathTCN=current_layer).

[0104] S323. If the shortest path is not found at the current level, continue processing the next lower TCN level.

[0105] Specifically, if no shortest path is found at the current level, this step will continue processing the next lower TCN level. For example, after failing at the level with a threshold of 0.8, the query will move down to the level with a threshold of 0.6.

[0106] S33. Confirm the optimal path and terminate the search.

[0107] Specifically, the first path found comes from the highest effective TCN level, and is therefore the shortest path with the highest topological connectivity (shortest_path).

[0108] The entire search loop is terminated, skipping all remaining lower TCN levels. For example, once a valid path is found at level 0.4, this step does not check levels 0.2 or lower. This early termination mechanism significantly improves the algorithm's efficiency, especially for large-scale networks.

[0109] S34. If no path is found at any level, return null.

[0110] S4. Based on the shortest path, obtain the high topological connectivity of the shortest path.

[0111] Specifically, it returns the shortest path with high topological connectivity found, along with the path's topological connectivity.

[0112] For example, return the shortest path with high topological connectivity, shortest_path=[TP53, BRCA1, FANCD2, MYC], and its path TCN value, pathTCN=0.6.

[0113] This application defines a topology common neighbor (TCN) index, enabling the measurement of the propagation potential between biomolecules in gene regulatory networks. Unlike existing studies, this approach considers both path length and the topology common neighbor index to ensure both propagation speed and relative stability. Furthermore, this application reveals the crucial role of potential propagation pathways in driving disease cascade effects and provides a network-based predictive framework for identifying potential therapeutic targets.

[0114] The above description is merely an embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for fast query of high topological connectivity shortest propagation path, characterized in that, The method comprises the following steps: S1. Obtain TCN values between biomolecules in a given gene regulatory network, and sort the biomolecule pairs according to the TCN values to generate a hierarchical structure; S2. Based on the input starting biomolecule and target biomolecule, perform a breadth-first search strategy to obtain the shortest path in each hierarchy that meets the TCN hierarchy constraint; S3. Based on the hierarchy threshold list in the hierarchical structure, search the hierarchies from top to bottom to obtain the shortest path in all hierarchies; S4. Based on the shortest path, obtain the high topological connectivity of the shortest path.

2. The method of claim 1, wherein, The method of step S1 comprises the following steps: S11. Initialize a dictionary structure to store the TCN values of each edge; S12. Obtain the TCN values of each edge in the gene regulatory network, and store the TCN values in the dictionary structure after precision processing; S13. Based on the dictionary structure, obtain the neighbor set of the biomolecules at both ends of the edge; S14. Sort the TCN values from large to small, and extract all different TCN values; S15. Based on the threshold list and the different TCN values, generate the hierarchical structure.

3. The method of claim 1, wherein, The method of step S2 comprises the following steps: S21. Input validity check, verify whether the starting biomolecule belongs to the corresponding hierarchy; S22. Initialize a queue and a path record dictionary; S23. Based on the breadth-first search, expand the search layer by layer by traversing the neighbors of the current biomolecule, registering unvisited biomolecules, and updating the queue until the target biomolecule is found; S24. If the current biomolecule is equal to the target biomolecule, reconstruct the path in reverse; generate the complete path from the target biomolecule to the starting biomolecule by backtracking the predecessor relationship in the path record dictionary; S25. Verify the validity of the path by checking whether the target biomolecule in the path is the starting biomolecule to ensure that the generated path is correct and complete.

4. The method of claim 1, wherein, The method of step S23 comprises the following steps: S231. Extract the current biomolecule and judge the termination condition; S232. Traverse the neighbors of the current biomolecule in the given hierarchy; S233. For each neighbor biomolecule of the current biomolecule, if it is not recorded in the path record dictionary, update the predecessor relationship and update the queue; S234. Repeat the above steps to process the biomolecules in the queue one by one until the target biomolecule is taken out.

5. The method of claim 1, wherein, The method of step S3 comprises the following steps: S31. Based on the hierarchy threshold, process the hierarchies one by one in descending order; S32. Search for the shortest path in the current hierarchy; S33. Confirm the optimal path and terminate the search; S34. If no path is found in all hierarchies, return an empty value.

6. The method of claim 4, wherein, The method of step S32 comprises the following steps: S321. Based on the breadth-first search strategy, set the specified hierarchy as the current processing hierarchy, and search for the shortest path in the current processing hierarchy; S322. If the shortest path is found in the current hierarchy, return the shortest path as the query result, and the topological connectivity of the shortest path is the current hierarchy threshold; S323. If the shortest path is not found in the current hierarchy, continue to process the next lower TCN hierarchy.

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