A method and device for dividing Hi-C data topologically related structural domains

Abstract

The present invention discloses a method and device for partitioning Hi-C data topologically related domains, the method comprising: obtaining Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, preprocessing the raw observation data to obtain a normalized Hi-C contact matrix; based on the relationship between Hi-C data contact frequency and spatial distance, converting the Hi-C contact matrix into a distance matrix between each genomic site; calculating the shortest distance between genomic sites using a shortest path algorithm, retaining the partial value with the smallest distance for each site to obtain a spatial distance map of the genome; clustering the sites in the spatial distance map of the genome using a clustering algorithm to obtain TAD partitioning of the Hi-C data. The present invention achieves the partitioning of chromatin TADs by normalizing, converting, and calculating the shortest path and genomic site clustering of Hi-C data.

Description

Technical Field

[0001] The present invention relates to the field of computational biology technology, and in particular to a method and device for partitioning Hi-C data topologically related structural domains. Background Art

[0002] Hi-C is a high-throughput chromatin conformation capture technology that can capture genome-wide chromosome interactions through formaldehyde fixation, enzyme digestion, circular ligation, sequence fragmentation, library construction and sequencing, and mapping them to a reference genome. Hi-C technology uses high-throughput sequencing technology to generate genome-wide, large-scale intra-chromosomal and inter-chromosomal interaction (contact frequency) data, which can describe the spatial structure within the genome. Deeper sequencing of interacting DNA fragments can obtain higher-resolution Hi-C data, showing more and finer structural information. With the continuous development and maturity of its technology and the sharp decline in sequencing prices, it has gradually become a commonly used technology for studying genomes in the literature.

[0003] The eukaryotic genome folds into a well-defined spatially organized region within the cell nucleus. Three-dimensional genomic research has been gaining momentum in recent years. Through the study of genomic sequencing data, such as Hi-C, the hierarchical structure of the genome has been gradually revealed. From largest to smallest, this hierarchical structure includes active and inactive compartments (A / B compartments), topologically associated domains (TADs), and chromatin loops.

[0004] TAD has recently attracted much attention in the literature. It is characterized by a high level of interaction within the domain and a low level of interaction outside the domain at the genomic site on the chromosome. This structure performs important biological functions. The average length of TAD is about 1Mbp, and different TADs are separated by insulators, and TADs are stable across cell lines. An important function of TAD is to form independent regions for gene regulation while isolating them from neighboring regions. The division of genomic TADs is very useful for studying gene regulation, genomic interactions and genomic function. TAD disruption may lead to serious diseases such as cancer. Therefore, it is very important to divide TADs based on the large amount of Hi-C data obtained experimentally. Research on TADs is beneficial to a deeper understanding of diseases.

[0005] Existing TAD identification methods are complex and diverse. However, clustering-based methods, such as ClusterTAD, mostly use Hi-C data at 40 kb resolution or lower for TAD delineation, resulting in low robustness and reliability relative to Hi-C data resolution. At ultra-high resolution, the sparsity of matrix data leads to poor clustering of samples within the feature space, reducing clustering accuracy. Therefore, TAD delineation methods at high resolution are a worthy research topic. Summary of the Invention

[0006] The present invention provides a method and apparatus for partitioning topologically related domains of Hi-C data to enhance the accuracy of TAD partitioning of high-resolution Hi-C data and achieve multi-level TAD partitioning.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] In one aspect, the present invention provides a method for partitioning Hi-C data into topologically related domains, comprising:

[0009] Obtaining Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, and preprocessing the raw observation data using the vector to obtain a normalized Hi-C contact matrix;

[0010] Based on the functional relationship between the contact frequency and spatial distance of Hi-C data, the Hi-C contact matrix is ​​converted into a distance matrix between each site in the genome;

[0011] The shortest distance between genomic sites is calculated using a preset shortest path algorithm, and the minimum distance value is retained for each site to obtain a spatial distance map of the genome;

[0012] The sites in the spatial distance map of the genome are clustered using a preset clustering algorithm to obtain topologically related structural domain divisions of the Hi-C data.

[0013] Furthermore, the resolution of the original observation data of Hi-C genome sequencing is not less than 50 kb.

[0014] Furthermore, preprocessing the original observation data using the vector includes:

[0015] The values ​​in the raw observation data of the Hi-C genome sequencing are divided by the corresponding norm factors in the vector.

[0016] Furthermore, the functional relationship between the contact frequency and spatial distance of the Hi-C data is:

[0017]

[0018] Where f represents the contact frequency of Hi-C data, d represents the spatial distance, and α is the preset conversion parameter.

[0019] Furthermore, the preset shortest path algorithm is the Floyd Warshall algorithm.

[0020] Furthermore, the partial values ​​with the smallest distance retained for each site are the number of retained values ​​determined using the golden section search algorithm; the number of retained values ​​determined using the golden section search algorithm includes:

[0021] The number of retention values ​​is set to 10% of the total number of chromosome sites in the Hi-C data at the resolution used, that is, V keep =length(D) / 10, where D is the distance matrix and length(D) represents the number of rows in the distance matrix, i.e. the number of chromosome sites. Then a unimodal objective function is defined:

[0022]

[0023] Among them, V TAD Represents the value describing the TAD structure, V LongeRange Indicates long-range interactions;

[0024] The single-peak objective function value is calculated within the search interval, and the known range of the maximum value of the single-peak objective function is continuously narrowed by the golden section search algorithm, so as to find the maximum value of the function and obtain the number of retained values.

[0025] Furthermore, the preset clustering algorithm is the DBSCAN algorithm;

[0026] Clustering the sites in the spatial distance map of the genome using a clustering algorithm includes:

[0027] Calculate the distance between adjacent samples and count their distribution. The result shows a single-peak distribution as the distance increases. According to the sample distance distribution, the peak value is selected as the neighborhood radius Eps parameter.

[0028] The minimum number of points within the radius, MinPts, was calculated by dividing the resolution of Hi-C genome sequencing data and the size of the topologically related domain structure;

[0029] Based on Eps and MinPts, the sites in the spatial distance map are clustered using the DBSCAN algorithm.

[0030] On the other hand, the present invention also provides a device for dividing Hi-C data topology-related structural domains, comprising:

[0031] a data processing module, configured to obtain Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, and preprocess the raw observation data using the vector to obtain a normalized Hi-C contact matrix;

[0032] A distance map calculation module is used to convert the Hi-C contact matrix into a distance matrix between genomic sites based on the functional relationship between Hi-C data contact frequency and spatial distance; calculate the shortest distance between genomic sites using a preset shortest path algorithm, retain the partial value with the smallest distance for each site, and obtain a spatial distance map of the genome;

[0033] The clustering module is used to cluster the sites in the spatial distance map of the genome using a preset clustering algorithm to obtain topologically related structural domain divisions of the Hi-C data.

[0034] On the other hand, the present invention further provides an electronic device, comprising a processor and a memory; wherein the memory stores at least one instruction, and the instruction is loaded and executed by the processor to implement the above method.

[0035] In yet another aspect, the present invention further provides a computer-readable storage medium, wherein the storage medium stores at least one instruction, and the instruction is loaded and executed by a processor to implement the above method.

[0036] The beneficial effects brought about by the technical solution provided by the present invention include at least:

[0037] The technical solution provided by the present invention divides Hi-C data into topologically related domains through a clustering method. The TAD contact data is converted into spatial distances through a conversion function, and the sparse interaction data at high resolution is converted into a spatial distance map describing spatial proximity using the shortest path algorithm. Using the spatial distance map as the clustering input satisfies the physical spatial distribution characteristics of TAD, so that the sparse high-resolution Hi-C data can be fully utilized to obtain more accurate TAD divisions. Moreover, the present invention can use Hi-C data at a resolution of 50kb and higher for division. The TAD division process of Hi-C data at a resolution of 50kb to 5kb is stable, and a hierarchical division of TAD at different observation scales can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0039] Figure 1 Flowchart of a method for partitioning Hi-C data topologically related structural domains provided by an embodiment of the present invention;

[0040] Figure 2 Detailed flowchart of the method for partitioning Hi-C data topology-related structural domains provided by an embodiment of the present invention;

[0041] Figure 3 4 is a system block diagram of a device for partitioning Hi-C data topology-related structural domains provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0042] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0043] First embodiment

[0044] This embodiment provides a method for dividing Hi-C data topology-related structural domains. The method can be implemented by an electronic device. The execution process of the method is as follows: Figure 1 As shown, the following steps are included:

[0045] S1, obtaining Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, and using the vector to preprocess the raw observation data to obtain a normalized Hi-C contact matrix;

[0046] The resolution of the original observation data of Hi-C genome sequencing is 50kb or higher. The vector is used to process the systematic deviation of the original observation data of Hi-C genome sequencing, thereby performing matrix balance on the original observation data to obtain a standardized Hi-C contact matrix. Specifically, in this embodiment, the vector used to normalize the original observation matrix can be calculated using commonly used Hi-C data normalization methods such as Knight-Ruiz (KR) or Vanilla-Coverage (VC).

[0047] The KR normalization method uses the symmetric and non-negative properties of the Hi-C contact matrix to perform diagonal scaling based on this property and uses the conjugate gradient iteration method to balance the matrix so that the sum of each row and column element of the matrix is ​​1;

[0048] The VC normalization method divides each element of the Hi-C contact matrix first by the sum of the corresponding row and then by the sum of the corresponding column, resulting in a normalized matrix.

[0049] Specifically, if Figure 2As shown, this embodiment uses the vector to preprocess the original observation data as follows: the values ​​in the Hi-C genome sequencing original observation data are divided by the corresponding norm factors in the KR normalization vector to perform a noise removal operation to obtain a normalized Hi-C contact matrix F.

[0050] S2, based on the functional relationship between Hi-C data contact frequency and spatial distance, convert the Hi-C contact matrix into a distance matrix between each site in the genome;

[0051] The contact frequency and spatial distance of Hi-C data satisfy the following functional relationship:

[0052]

[0053] Where f represents the contact frequency of Hi-C data, d represents the spatial distance, and α is a conversion parameter. This conversion parameter can be selected based on the resolution, and its default value is 1 / 3.

[0054] Based on the above functional relationship, the contact matrix F is converted into the distance matrix D.

[0055] S3, calculate the shortest distance between genomic sites using a preset shortest path algorithm, retain the partial value with the smallest distance for each site, and obtain the spatial distance map of the genome;

[0056] like Figure 2 As shown, the shortest path algorithm is Floyd Warshall, which is used to solve the shortest path distance of a weighted graph. It loops through the vertices in the spatial distance matrix, and for positions where the distance value is infinite, checks whether the simple distance between a pair of vertices can be made smaller through the base point, and then updates the distance between the two points.

[0057] The Floyd-Warshall shortest path algorithm calculates the shortest distances between genomic sites. High-resolution Hi-C data is very sparse, as sequencing depth increases, and some spatially adjacent sites lack sequencing read pairs. This calculation step generates a matrix that reflects the proximity of sites in local space, facilitating subsequent inter-sample distance calculations. Furthermore, the use of a maximum-retention approach prevents long-range interactions from affecting TAD delineation after the shortest distance algorithm is applied.

[0058] Specifically, the method of retaining the minimum distance partial value for each site is to use the golden section search algorithm to determine the number of retained values. It should be noted that different numbers of points need to be retained at different resolutions to meet the needs of describing the structural information of TAD while avoiding the influence of long-range interactions on the demarcation of TAD boundaries. Based on this, the number of retained values ​​is set to 10% of the total number of chromosome sites in the Hi-C data at the resolution used, that is, V keep =length(D) / 10, where D is the distance matrix and length(D) represents the number of rows in the distance matrix, i.e. the number of chromosome sites. Then define a unimodal objective function:

[0059]

[0060] Among them, V TAD Indicates a value that can describe the TAD structure, with the linear distance between the two sites within 5 Mbp. LongeRange Indicates long-range interaction, where the linear distance between the two sites is greater than 10 Mbp.

[0061] The function value is calculated within the search interval. If σ does not reach the maximum value, the known range of the maximum value of the unimodal function (search range) is iteratively narrowed by the golden section search algorithm, and the new number of retained values ​​is searched. σ is recalculated based on this value until the maximum value of the function is found and the number of retained values ​​is obtained.

[0062] S4, clustering the sites in the spatial distance map of the genome using a preset clustering algorithm to obtain topologically related structural domain divisions of the Hi-C data.

[0063] Among them, such as Figure 2 As shown, the clustering algorithm is the density-based clustering method DBSCAN. The parameters of the DBSCAN algorithm use the spatial distance map as input. The neighborhood radius Eps parameter uses the golden section algorithm to search within a given range to find the optimal parameter. The minimum number of points within the radius MinPts is calculated by dividing the resolution of the Hi-C genome sequencing data and the size of the TAD structure. Specifically, the clustering algorithm is used to cluster the sites in the spatial distance map, including:

[0064] Calculate the distance between adjacent samples and count their distribution. The result shows a single-peak distribution as the distance increases. According to the sample distance distribution, the peak value is selected as the neighborhood radius Eps parameter; then the Eps neighborhood of the sample site p is defined as: N Eps (p)={q∈D|dist(p,q)≤Eps};

[0065] In this embodiment, the sample distance calculation function of the density-based clustering method DBSCAN uses the angle cosine distance dist(p,q)=cosθ. In two-dimensional space, the angle cosine formula between vectors A(x1,y1) and B(x2,y2) is Extending it to n-dimensional space, for two n-dimensional sample points p(x 11 ,x 12 ,…,x 1n ) and q(x 11 ,x 12 ,…,x 1n ), the calculation formula is:

[0066]

[0067] The minimum number of points within the radius, MinPts, is calculated by dividing the resolution of Hi-C genomic sequencing data and the size of topologically associated domains. For example, if the data resolution is 5kb and you want to identify topologically associated domains of 500kb or greater, MinPts should be 100. If the number of sample points within the neighborhood of a given object, Eps, is greater than or equal to MinPts, the object is considered a core object.

[0068] By properly setting the two important parameters of the DBSCAN algorithm, the sites in the spatial distance map of the genome are clustered, and the classification labels are obtained and displayed. The specific process is as follows:

[0069] Step 1: Check the sample point p. If p has not been processed, check its neighborhood. If the number of points in the neighborhood of the sample point p is not less than the minimum number of points within the radius, MinPts, then create a new cluster C, and all points within the neighborhood radius are added to the candidate set N. If the number of points in the neighborhood of the sample point p is less than the minimum number of points within the radius, MinPts, then mark this sample as a noise point.

[0070] Step 2: For all objects q in the candidate set N that have not been processed, check their neighborhoods. If the number of points contained in them is not less than MinPts, add these objects to N. If q is not classified into any cluster, add q to cluster C.

[0071] Step 3: Repeat step 2 above and continue to check the unprocessed objects in N until the candidate set N is empty, then stop.

[0072] Repeat steps 1 to 3 above and stop when all samples are classified into a cluster or marked as noise.

[0073] In summary, the technical solution of this embodiment divides the Hi-C data into topologically related domains through a clustering method. The TAD contact data obtains spatial distances through a conversion function, and the sparse interaction data at high resolution is converted using the shortest path algorithm to obtain a spatial distance map describing spatial proximity. Using the spatial distance map as the clustering input satisfies the physical spatial distribution characteristics of TAD, so that the sparse high-resolution Hi-C data can be fully utilized to obtain more accurate TAD divisions. Moreover, the present invention can use Hi-C data at a resolution of 50kb and higher for division. The TAD division process of Hi-C data at a resolution of 50kb to 5kb is stable, and a hierarchical division of TAD at different observation scales can be obtained.

[0074] Second embodiment

[0075] This embodiment provides a device for dividing Hi-C data topology-related structural domains. The system structure of the device for dividing Hi-C data topology-related structural domains is as follows: Figure 3 As shown, it includes the following modules:

[0076] a data processing module, configured to obtain Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, and preprocess the raw observation data using the vector to obtain a normalized Hi-C contact matrix;

[0077] A distance map calculation module is used to convert the Hi-C contact matrix into a distance matrix between genomic sites based on the functional relationship between Hi-C data contact frequency and spatial distance; calculate the shortest distance between genomic sites using a preset shortest path algorithm, retain the partial value with the smallest distance for each site, and obtain a spatial distance map of the genome;

[0078] The clustering module is used to cluster the sites in the spatial distance map of the genome using a preset clustering algorithm to obtain topologically related structural domain divisions of the Hi-C data.

[0079] The apparatus for partitioning Hi-C data topology-related structural domains of this embodiment corresponds to the method for partitioning Hi-C data topology-related structural domains of the first embodiment described above. The functions implemented by the functional modules in the apparatus for partitioning Hi-C data topology-related structural domains of this embodiment correspond one-to-one to the process steps in the method for partitioning Hi-C data topology-related structural domains of the first embodiment described above. Therefore, these functions are not further described here.

[0080] Third embodiment

[0081] This embodiment provides an electronic device, which includes a processor and a memory; wherein the memory stores at least one instruction, and the instruction is loaded and executed by the processor to implement the method of the first embodiment.

[0082] The electronic device may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) and one or more memories, wherein the memory stores at least one instruction, which is loaded by the processor to execute the above method.

[0083] Fourth embodiment

[0084] This embodiment provides a computer-readable storage medium storing at least one instruction, which is loaded and executed by a processor to implement the method of the first embodiment described above. The computer-readable storage medium may be a ROM, random access memory, CD-ROM, magnetic tape, floppy disk, or optical data storage device. The instructions stored therein can be loaded by a processor in a terminal to execute the method described above.

[0085] Furthermore, it should be noted that the present invention may be provided as a method, apparatus, or computer program product. Thus, embodiments of the present invention may take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention may take the form of a computer program product embodied on one or more computer-usable storage media containing computer-usable program code.

[0086] The embodiments of the present invention are described with reference to the flowcharts and / or block diagrams of the methods, terminal devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the process in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0087] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device, so that a series of operation steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for implementing the process in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0088] It should also be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or terminal device comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or terminal device comprising the element.

[0089] Finally, it should be noted that the above is a preferred embodiment of the present invention. It should be noted that although the preferred embodiment of the present invention has been described, it is clear that those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles of the present invention. Such improvements and modifications should also be considered as within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the embodiments of the present invention.

Claims

1. A method for partitioning topologically related structural domains in Hi-C data, characterized in that: include: Obtaining Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, and preprocessing the raw observation data using the vector to obtain a normalized Hi-C contact matrix; Based on the functional relationship between the contact frequency and spatial distance of Hi-C data, the Hi-C contact matrix is ​​converted into a distance matrix between each site in the genome; The shortest distance between genomic sites is calculated using a preset shortest path algorithm, and the minimum distance value is retained for each site to obtain a spatial distance map of the genome; Clustering the sites in the spatial distance map of the genome using a preset clustering algorithm to obtain topologically related structural domain divisions of the Hi-C data; The resolution of the original observation data of Hi-C genome sequencing is not less than 50 kb; Preprocessing the original observation data using the vector includes: Dividing the value in the Hi-C genome sequencing raw observation data by the corresponding norm factor in the vector; The functional relationship between the contact frequency and spatial distance of the Hi-C data is: Where f represents the contact frequency of Hi-C data, d represents the spatial distance, and α is the preset conversion parameter; The preset shortest path algorithm is the Floyd Warshall algorithm; The number of retained values ​​for each site with the smallest distance is determined by using the golden section search algorithm; the number of retained values ​​determined by using the golden section search algorithm includes: The number of retention values ​​is set to 10% of the total number of chromosome sites in the Hi-C data at the resolution used, that is, V keep =length(D) / 10; where D is the distance matrix and length(D) represents the number of rows in the distance matrix, i.e. the number of chromosome sites; then a unimodal objective function is defined: Among them, V TAD Represents the value describing the TAD structure, V LongeRange Indicates long-range interactions; Calculate the single-peak objective function value within the search interval, and continuously narrow the known range of the maximum value of the single-peak objective function through the golden section search algorithm, so as to find the maximum value of the function and obtain the number of retained values; The preset clustering algorithm is the DBSCAN algorithm; Clustering the sites in the spatial distance map of the genome using a clustering algorithm includes: Calculate the distance between adjacent samples and count their distribution. The result shows a single-peak distribution as the distance increases. According to the sample distance distribution, the peak value is selected as the neighborhood radius Eps parameter. The minimum number of points within the radius, MinPts, was calculated by dividing the resolution of Hi-C genome sequencing data and the size of the topologically related domain structure; Based on Eps and MinPts, the sites in the spatial distance map are clustered using the DBSCAN algorithm.

2. A device for partitioning Hi-C data topologically related structural domains, characterized in that: include: a data processing module, configured to obtain Hi-C genome sequencing raw observation data and a vector for normalizing the raw observation matrix, and preprocess the raw observation data using the vector to obtain a normalized Hi-C contact matrix; A distance map calculation module is used to convert the Hi-C contact matrix into a distance matrix between various sites in the genome based on the functional relationship between the contact frequency and spatial distance of the Hi-C data; The shortest distance between genomic sites is calculated using a preset shortest path algorithm, and the minimum distance value is retained for each site to obtain a spatial distance map of the genome; A clustering module is used to cluster the sites in the spatial distance map of the genome using a preset clustering algorithm to obtain topologically related structural domain divisions of the Hi-C data; The resolution of the original observation data of Hi-C genome sequencing is not less than 50 kb; Preprocessing the original observation data using the vector includes: Dividing the value in the Hi-C genome sequencing raw observation data by the corresponding norm factor in the vector; The functional relationship between the contact frequency and spatial distance of the Hi-C data is: Where f represents the contact frequency of Hi-C data, d represents the spatial distance, and α is the preset conversion parameter; The preset shortest path algorithm is the Floyd Warshall algorithm; The number of retained values ​​for each site with the smallest distance is determined by using the golden section search algorithm; the number of retained values ​​determined by using the golden section search algorithm includes: The number of retention values ​​is set to 10% of the total number of chromosome sites in the Hi-C data at the resolution used, that is, V keep =length(D) / 10; where D is the distance matrix and length(D) represents the number of rows in the distance matrix, i.e. the number of chromosome sites; then a unimodal objective function is defined: Among them, V TAD Represents the value describing the TAD structure, V LongeRange Indicates long-range interactions; Calculate the single-peak objective function value within the search interval, and continuously narrow the known range of the maximum value of the single-peak objective function through the golden section search algorithm, so as to find the maximum value of the function and obtain the number of retained values; The preset clustering algorithm is the DBSCAN algorithm; Clustering the sites in the spatial distance map of the genome using a clustering algorithm includes: Calculate the distance between adjacent samples and count their distribution. The result shows a single-peak distribution as the distance increases. According to the sample distance distribution, the peak value is selected as the neighborhood radius Eps parameter. The minimum number of points within the radius, MinPts, was calculated by dividing the resolution of Hi-C genome sequencing data and the size of the topologically related domain structure; Based on Eps and MinPts, the sites in the spatial distance map are clustered using the DBSCAN algorithm.

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