Prediction method of spatial transcriptomics, and prediction system and storage medium thereof

Abstract

The application discloses a spatial transcriptomics prediction method, a prediction system thereof and a storage medium. The spatial transcriptomics prediction method comprises the following steps: confirming shared genes of spatial transcriptomics data and single-cell data; constructing a first expression matrix corresponding to the shared genes in the spatial transcriptomics data, constructing a second expression matrix corresponding to the shared genes in the single-cell data, and constructing a third expression matrix corresponding to unique genes in the single-cell data; constructing a similarity matrix between cells based on spatial information; inputting the above matrix into a target function, and performing iterative optimization by using the target function; and integrating the unique gene representation of the second single-cell data and the cell low-dimensional representation of the second spatial transcriptomics to predict undetected gene expression. The technical scheme of the application can effectively predict undetected genes, make the molecular mechanism analysis of biological samples more complete, and reduce the deviation in disease research.

Description

Technical Field

[0001] This invention relates to the field of biological detection technology, specifically to a spatial transcriptomics prediction method, prediction system, and computer-readable storage medium. Background Technology

[0002] Spatial transcriptomics (ST) technology provides a crucial tool for understanding cellular microenvironment heterogeneity by capturing the spatial location and gene expression information of cells in tissue sections. While imaging-based spatial transcriptomics can achieve single-cell resolution spatial localization, its gene detection throughput is limited, typically detecting only tens to hundreds of genes. This makes it difficult to obtain whole-genome expression profiles, resulting in incomplete analysis of the molecular mechanisms of biological samples and potentially introducing biases in disease research. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a spatial transcriptomics prediction method that can effectively predict undetected genes, making the molecular mechanism analysis of biological samples more complete and reducing bias in disease research.

[0004] This application provides a spatial transcriptomics prediction method, the prediction method comprising:

[0005] Acquire spatial transcriptomics data and single-cell data, and identify shared genes between the spatial transcriptomics data and the single-cell data;

[0006] Construct a first expression matrix corresponding to the shared genes in the spatial transcriptomics data, construct a second expression matrix corresponding to the shared genes in the single-cell data, and construct a third expression matrix corresponding to the unique genes in the single-cell data;

[0007] Construct a similarity matrix between cells based on spatial information;

[0008] The first expression matrix, the second expression matrix, the third expression matrix, and the similarity matrix are input into the objective function to obtain the low-dimensional representation of shared genes in the first spatial transcriptomics, the low-dimensional representation of unique genes in the first single-cell data, the low-dimensional representation of cells in the first spatial transcriptomics, and the low-dimensional representation of cells in the first single-cell data.

[0009] The shared gene low-dimensional representations of the first spatial transcriptomics, the unique gene low-dimensional representations of the first single-cell data, the cell low-dimensional representations of the first spatial transcriptomics, and the cell low-dimensional representations of the first single-cell data are iteratively optimized using the objective function to obtain the shared gene low-dimensional representations of the second spatial transcriptomics, the unique gene low-dimensional representations of the second single-cell data, the cell low-dimensional representations of the second spatial transcriptomics, and the cell low-dimensional representations of the second single-cell data.

[0010] The unique gene representations from the second single-cell data are integrated with the low-dimensional cellular representations from the second spatial transcriptomics to predict the expression of undetected genes.

[0011] In one aspect, the step of iterative optimization using the objective function includes:

[0012] The objective function is solved iteratively using the Lagrange multiplier method.

[0013] In one aspect, the step of iteratively solving the objective function using the Lagrange multiplier method includes:

[0014] The objective function is solved iteratively using the Lagrange multiplier method. The iteration terminates when the change in the objective function value is less than a preset stopping threshold, wherein the stopping threshold is in the range of 10. -5 Up to 10 -7 between.

[0015] In one aspect, the step of constructing a similarity matrix between cells based on spatial information includes:

[0016] Based on spatial information, a similarity matrix between cells is constructed using the symmetric K-nearest neighbor algorithm.

[0017] In one aspect, the objective function is defined as follows:

[0018]

[0019] Where F is the norm, tr represents the trace of the matrix, the first expression matrix is ​​X1, the second expression matrix is ​​X2, the third expression matrix is ​​X3, X1≈W1H1, X2≈W1H2, X3≈W2H2, W1 is the low-dimensional representation of shared genes in the first spatial transcriptomics, H1 is the low-dimensional representation of cells in the first spatial transcriptomics, H2 is the low-dimensional representation of cells in the first single-cell data, W2 is the low-dimensional representation of unique genes in the first single-cell data, θ1, θ2, λ1, and λ2 are hyperparameters, L1 is the graph Laplacian matrix, T is the transpose of the corresponding matrix, j represents the j-th column of the matrix, h j The j-th column, h′, represents the low-dimensional cellular representation of first-space transcriptomics.j It is the j-th column of the low-dimensional representation of the cell in the first single-cell data.

[0020] In one aspect, after obtaining the shared gene low-dimensional representations of the second spatial transcriptomics, the unique gene low-dimensional representations of the second single-cell data, the cellular low-dimensional representations of the second spatial transcriptomics, and the cellular low-dimensional representations of the second single-cell data, the method further includes:

[0021] Integrating the shared gene low-dimensional representations from the second spatial transcriptomics and the cellular low-dimensional representations from the second spatial transcriptomics yields denoised expression.

[0022] Furthermore, to address the aforementioned problems, this application also provides a spatial transcriptomics prediction system, the prediction system comprising:

[0023] The acquisition module is used to acquire spatial transcriptomics data and single-cell data, and to identify shared genes between the spatial transcriptomics data and the single-cell data;

[0024] The construction module is used to construct a first expression matrix corresponding to the shared gene in the spatial transcriptomics data, construct a second expression matrix corresponding to the shared gene in the single-cell data, construct a third expression matrix corresponding to the unique gene in the single-cell data, and construct a similarity matrix between cells based on spatial information.

[0025] An iterative module is used to input the first expression matrix, the second expression matrix, the third expression matrix, and the similarity matrix into an objective function to obtain low-dimensional representations of shared genes in first spatial transcriptomics, low-dimensional representations of unique genes in first single-cell data, low-dimensional representations of cells in first spatial transcriptomics, and low-dimensional representations of cells in first single-cell data. The module then iteratively optimizes these low-dimensional representations using the objective function to obtain low-dimensional representations of shared genes in second spatial transcriptomics, low-dimensional representations of unique genes in second single-cell data, low-dimensional representations of cells in second spatial transcriptomics, and low-dimensional representations of cells in second single-cell data.

[0026] An integration module is used to integrate the unique gene representations of the second single-cell data with the low-dimensional cellular representations of the second spatial transcriptomics to predict the expression of undetected genes.

[0027] In one aspect, the iterative module is also used to iteratively solve the objective function using the Lagrange multiplier method.

[0028] In one aspect, the building module is also used to construct a similarity matrix between cells based on spatial information using a symmetric K-nearest neighbor algorithm.

[0029] To address the aforementioned problems, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the prediction method described above.

[0030] The beneficial effects of this invention are reflected in the following aspects: Shared genes retain the cross-modal commonalities between spatial transcriptomics data and single-cell data on the one hand, and can isolate unique genes from single-cell data on the other. By decoupling and decomposing the first, second, and third expression matrices, the spatial specificity of spatial transcriptomics data is more realistically reflected. A similarity matrix is ​​constructed using spatial information, transforming spatial locations into a computable form, laying the foundation for introducing spatial constraints into the subsequent objective function, and ensuring that spatially adjacent cells maintain expression similarity in low-dimensional representations. This achieves the synergistic preservation of undetected gene prediction and spatial heterogeneity. Iterative optimization using the objective function integrates the unique gene representations of the second single-cell data with the low-dimensional cellular representations of the second spatial transcriptomics, predicting the expression of undetected genes, resulting in a more complete analysis of the molecular mechanisms of biological samples and reducing bias in disease research. Attached Figure Description

[0031] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0032] Figure 1 This is a schematic diagram of the prediction method for spatial transcriptomics in this application;

[0033] Figure 2 For this application Figure 1 A schematic diagram of the iterative solution process for the objective function;

[0034] Figure 3 For this application Figure 2 A schematic diagram illustrating the setting of a stopping threshold for solving the objective function;

[0035] Figure 4 For this application Figure 1 A schematic diagram illustrating the steps involved in constructing similar matrices;

[0036] Figure 5 This is a schematic diagram of the process steps for integrating and forming a denoised expression in the spatial transcriptomics prediction method of this application;

[0037] Figure 6 The graph shows the performance of the prediction method in this application compared with other methods at the gene level.

[0038] Figure 7 The graph shows the performance of the prediction method in this application compared with other methods at the cellular level.

[0039] Figure 8 This is a schematic diagram of the spatial transcriptomics prediction system of this application.

[0040] Figure descriptions: 100, Acquisition module; 200, Construction module; 300, Iteration module; 400, Integration module. Detailed Implementation

[0041] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0042] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0043] See Figure 1 As shown, this application provides a prediction method for spatial transcriptomics, the prediction method comprising:

[0044] Step S10 involves acquiring spatial transcriptomics data and single-cell data, and identifying shared genes between the two datasets. Spatial transcriptomics data typically comes from imaging-based techniques (such as osmFISH and smFISH), while single-cell data usually comes from single-cell sequencing technology and typically includes the full transcriptome expression values ​​of a single cell. For example, genes present in both spatial transcriptomics data and single-cell data can be screened through gene name comparison; these are considered shared genes.

[0045] Step S20: Construct a first expression matrix corresponding to shared genes in the spatial transcriptomics data, a second expression matrix corresponding to shared genes in the single-cell data, and a third expression matrix corresponding to unique genes in the single-cell data. The first expression matrix extracts the expression values ​​of shared genes from the spatial transcriptomics data and constructs a matrix. The second expression matrix extracts the expression values ​​of the same shared genes from the single-cell data and constructs a matrix, reflecting the expression pattern of shared genes in the single-cell data. The third expression matrix extracts the expression values ​​of genes not detected in the spatial transcriptomics data (i.e., unique genes) from the single-cell data and constructs a matrix, representing the high-dimensional gene information unique to the single-cell data. Subsequently, these three types of data are integrated through a model to preserve cross-modal commonalities and utilize the gene diversity of single cells to predict undetected genes in the spatial transcriptomics data.

[0046] Step S30: Construct a similarity matrix between cells based on spatial information. Spatial information can be understood as the spatial location of cells, which can be two-dimensional coordinates. The spatial location of each cell, such as coordinates, is obtained from spatial transcriptomics data; these coordinates reflect the cell's original position in the tissue slice. Based on the spatial coordinates, the symmetric K-nearest neighbors (KNN) algorithm is used to calculate the proximity relationships between cells. The similarity matrix can also be converted into a graph Laplacian matrix for use as a spatial constraint term in the subsequent objective function.

[0047] Step S40: Input the first expression matrix, the second expression matrix, the third expression matrix, and the similarity matrix into the objective function to obtain the low-dimensional representation of shared genes in the first spatial transcriptomics, the low-dimensional representation of unique genes in the first single-cell data, the low-dimensional representation of cells in the first spatial transcriptomics, and the low-dimensional representation of cells in the first single-cell data; the shared genes in spatial transcriptomics can also be expressed as the shared genes in single-cell data, and can be understood as the same concept.

[0048] More specifically, the data is decomposed through an objective function to generate initial values ​​for low-dimensional representations, namely, low-dimensional representations of shared genes in the first spatial transcriptomics, low-dimensional representations of unique genes in the first single-cell data, low-dimensional representations of cells in the first spatial transcriptomics, and low-dimensional representations of cells in the first single-cell data, providing starting data for subsequent optimization. It should be noted that a graph Laplacian matrix is ​​generated through a similarity matrix; the graph Laplacian matrix embeds spatial information and is then input into the objective function.

[0049] Step S50 involves iteratively optimizing the low-dimensional representations of shared genes, unique genes, and cells from the first spatial transcriptomics, using an objective function, to obtain the low-dimensional representations of shared genes, unique genes, and cells from the second spatial transcriptomics, as well as the low-dimensional representations of cells from the second single-cell data. By iteratively adjusting the low-dimensional representations and minimizing the objective function, a more accurate low-dimensional representation is obtained. During the iterative optimization process, spatial constraints ensure that spatially adjacent cells remain similar, thereby deeply embedding spatial information into the low-dimensional representation and providing more accurate spatial features for prediction.

[0050] Step S60 integrates the unique gene representations from the second single-cell data with the low-dimensional cellular representations from the second spatial transcriptomics to predict the expression of undetected genes. The predicted undetected genes retain the gene expression patterns from the single-cell data and conform to the spatial distribution patterns of the spatial transcriptomics data, enabling the prediction of undetected genes under spatial constraints.

[0051] In this embodiment, shared genes retain the cross-modal commonalities between spatial transcriptomics data and single-cell data while simultaneously isolating unique genes from single-cell data. By decoupling and decomposing the first, second, and third expression matrices, the spatial specificity of spatial transcriptomics data is more accurately reflected. A similarity matrix is ​​constructed using spatial information, transforming spatial locations into a computable form and laying the foundation for introducing spatial constraints into the subsequent objective function, ensuring that spatially adjacent cells maintain expression similarity in their low-dimensional representation. This achieves synergistic preservation of undetected gene prediction and spatial heterogeneity. Iterative optimization using the objective function integrates the unique gene representations of the second single-cell data with the low-dimensional cellular representations of the second spatial transcriptomics, predicting the expression of undetected genes. This leads to a more complete analysis of the molecular mechanisms of biological samples and reduces bias in disease research.

[0052] See Figure 2 As shown, the steps for iterative optimization using the objective function include:

[0053] Step S510 involves iteratively solving the objective function using the Lagrange multiplier method. The Lagrange multiplier method is a mathematical method for finding the extrema of a function under equality constraints. By introducing Lagrange multipliers, the constraints are linked to the original objective function, constructing a new function, thereby obtaining the values ​​of each variable when the original function reaches its extremum. The Lagrange multiplier method derives the update rules for each variable by differentiating the objective function and setting the gradient to zero. Since the objective function involves multiple variables, an alternating optimization strategy is required: fixing other variables and updating each variable one by one until the objective function converges.

[0054] See Figure 3 As shown, the steps for iteratively solving the objective function using the Lagrange multiplier method include:

[0055] Step S511: Iterate the objective function using the Lagrange multiplier method. Terminate the iteration when the change in the objective function value is less than a preset stopping threshold. The stopping threshold is within the range of 10. -5 Up to 10 -7 In spatial transcriptomics undetected gene prediction models, the objective function needs to be iteratively optimized using the Lagrange multiplier method, progressively updating low-dimensional representation variables, including shared gene low-dimensional representations, unique gene low-dimensional representations, spatial transcriptomics cell low-dimensional representations, and single-cell data cell low-dimensional representations, so that the objective function converges to a sufficiently small value, and the magnitude of change in the objective function value is less than a preset stopping threshold. The stopping threshold can be 10. -5 It can also be 10 -6 Or 10 -7 .

[0056] See Figure 4 As shown, the steps for constructing a similarity matrix between cells based on spatial information include:

[0057] Step S310: Based on spatial information, a similarity matrix between cells is constructed using the symmetric K-nearest neighbor algorithm. This transforms the spatial location information of cells in spatial transcriptomics data into computable mathematical relationships, quantifies the spatial proximity between cells, and provides a basis for introducing spatial constraints into the subsequent objective function.

[0058] By constructing a similarity matrix using the symmetric K-nearest neighbor (KNN) algorithm, the biological relationship of spatial proximity can be transformed into matrix form, making it easier for the model to handle spatial constraints using linear algebra methods.

[0059] In this application, the objective function is defined as follows:

[0060] Then it satisfies:

[0061]

[0062] Where F is the norm, for example, the Frobenius norm; tr represents the trace of the matrix; the first expression matrix is ​​X1; the second expression matrix is ​​X2; and the third expression matrix is ​​X3. X1≈W1H1, X2≈W1H2, and X3≈W2H2. W1 is the low-dimensional representation of shared genes in the first spatial transcriptomics; H1 is the low-dimensional representation of cells in the first spatial transcriptomics; H2 is the low-dimensional representation of cells in the first single-cell data; W2 is the low-dimensional representation of unique genes in the first single-cell data; θ1, θ2, λ1, and λ2 are hyperparameters; L1 is the graph Laplacian matrix; and T is the transpose of the corresponding matrix, for example... H1 is the matrix transpose. j represents the j-th column of the matrix, h j The j-th column, h′, represents the low-dimensional cellular representation of first-space transcriptomics. j This is the j-th column of the low-dimensional representation of the cell in the first single-cell dataset. The graph Laplacian matrix L1 encodes spatial location information into a linear algebraic structure. Subsequently, the model constrains "spatially neighboring cells remain similar in their low-dimensional representations" to ensure that the predicted gene expression conforms to the true spatial distribution.

[0063] It is the square of the Frobenius norm. This represents the difference between X1 and the low-dimensional reconstruction matrix W1H1. The smaller the difference, the better the low-dimensional representation can restore X1. tr is the sum of the elements on the main diagonal of the matrix. This is the core of the spatial constraint term. Through trace operations, it combines the graph Laplacian matrix with the low-dimensional cellular representation of spatial transcriptomics, forcing similarity in the row vectors of spatially neighboring cells. Matrix transpose interchanges the rows and columns of the matrix. Furthermore, the choice of hyperparameters, for example, θ1 = 10... -1 θ2 is 10 -4 λ1 is 10 -5 λ2 is 10 1 .

[0064] After iterative solution, the low-dimensional representation of shared genes in second-space transcriptomics is as follows: The unique low-dimensional representation of genes in the second single-cell data is as follows: The low-dimensional cellular representation of second-space transcriptomics is as follows: The low-dimensional representation of the second single-cell data is as follows:

[0065] See Figure 5 As shown, after obtaining the shared gene low-dimensional representations of the second spatial transcriptomics, the unique gene low-dimensional representations of the second single-cell data, the cellular low-dimensional representations of the second spatial transcriptomics, and the cellular low-dimensional representations of the second single-cell data, the process further includes:

[0066] Step S70 integrates the shared gene low-dimensional representations from second-space transcriptomics and the cellular low-dimensional representations from second-space transcriptomics to obtain denoised expression data. Because raw spatial transcriptomics data often introduces noise due to technical limitations, gene expression values ​​deviate from the true biological state. Noise is filtered through objective function optimization, retaining the major biological variations that can be explained by low-dimensional features. By integrating the optimized shared gene low-dimensional representations from second-space transcriptomics and the cellular low-dimensional representations from second-space transcriptomics, technical noise in the raw spatial transcriptomics data is eliminated, resulting in a more realistic gene expression pattern.

[0067] The unique gene representation of the second single-cell data and the undetected gene expression of the low-dimensional cellular representation of the second spatial transcriptomics are as follows: Low-dimensional representation of shared genes in second-space transcriptomics and noisy expression in low-dimensional cellular representation of second-space transcriptomics.

[0068] It should be further noted that the prediction method of this application can be embedded in a learning model. After inputting spatial transcriptomics data, single-cell data and spatial information into the model, it outputs undetected genes and denoised expression.

[0069] It should also be noted that the prediction method of this application can also save running time. On a dataset of 33 genes, compared with other methods, the output results take 14 seconds, and on a dataset of 347 genes, it only takes 306 seconds, which can save computation time.

[0070] Secondly, compared to existing computational methods that mostly only enhance gene throughput while ignoring technical noise in the data itself, this application simultaneously enhances imaging-based spatial transcriptome sequencing technology from two dimensions: removing measurement data noise and increasing gene throughput. Furthermore, this application can fully utilize spatial information to enhance imaging-based spatial transcriptomics data, while existing computational methods lack the participation of spatial information. Finally, when predicting undetected genes, this application comprehensively considers both spatial transcriptomics data and single-cell datasets. Compared to existing computational methods that heavily rely on single-cell datasets, the prediction results of this application avoid bias towards the distribution of single-cell datasets and the loss of gene expression patterns related to spatial information.

[0071] See Figure 6 As shown, Figure 6 This section displays the accuracy scores of different algorithms on various experimental datasets. The horizontal axis represents different experimental data types, including osmFISH_Z (osmFISH_Zeisel), osmFISH_A (osmFISH_Allen), seqFISH, MERFISH, and Exseq, which are different spatial transcriptomics experimental techniques or dataset names. The vertical axis represents the accuracy score, ranging from 0.2 to 1.0, which measures the algorithm's accuracy performance; a higher score indicates better algorithm performance.

[0072] Different colors represent different algorithms. Red represents EDGES, which is the prediction method of this application. Other calculation methods are represented by orange for Tangram, blue for SpaGE, yellow for stPlus, and green for LIGER.

[0073] The prediction method EDGES (red) in this application generally has a high median on various experimental data, and most data points are concentrated in the high-score region, indicating that the EDGES algorithm has excellent and stable accuracy on different experimental data.

[0074] Tangram (orange) performed second overall, with a high median on some experimental data, but underperformed EDGES on others, showing slightly lower stability. SpaGE (blue), stPlus (yellow), and LIGER (green) algorithms had relatively low medians on most experimental data, with data points mostly distributed in lower score regions, indicating that their overall accuracy was lower than EDGES, especially the LIGER algorithm, which scored low on multiple experimental datasets. In conclusion, the prediction method proposed in this application showed the best accuracy and stability on various spatial transcriptomics experimental data.

[0075] See Figure 7 As shown, this is a bar chart displaying the performance of different algorithms under four evaluation metrics (Homo, NMI, AMI, ARI). The values ​​on the horizontal axis range from 0.0 to 0.3, representing the scores under different evaluation metrics.

[0076] The vertical axis lists four evaluation metrics: Homo, NMI, AMI, and ARI.

[0077] Different colored bars represent different algorithms. The prediction method in this application is EDGES (red), and other methods are: Tangram (orange), SpaGE (blue), stPlus (yellow), and LIGER (green).

[0078] The prediction method EDGES (red) in this application scores highly across the four evaluation metrics of Homo, NMI, AMI, and ARI, and its scores are significantly higher than other algorithms across all four metrics, indicating that the algorithm performs outstandingly in all evaluations.

[0079] Tangram (orange) scores relatively consistently across the four evaluation metrics, but overall falls below EDGES, showing a fairly balanced performance across different metrics. SpaGE (blue) scores fluctuate across different metrics, generally lower than EDGES, but slightly higher than Tangram in some metrics. stPlus (yellow) scores also vary across different metrics, generally at a below-average level, lower than EDGES and SpaGE. LIGER (green) scores generally low across the four evaluation metrics, ranking relatively low among the algorithms.

[0080] In summary, the prediction method EDGES algorithm proposed in this application performs best under these four evaluation metrics, significantly outperforming other algorithms.

[0081] See Figure 8 As shown, this application also provides a spatial transcriptomics prediction system, which includes: an acquisition module 100, a construction module 200, an iteration module 300, and an integration module 400.

[0082] The acquisition module 100 is used to acquire spatial transcriptomics data and single-cell data, and to identify shared genes in the spatial transcriptomics data and single-cell data.

[0083] The construction module 200 is used to construct the first expression matrix corresponding to shared genes in spatial transcriptomics data, the second expression matrix corresponding to shared genes in single-cell data, the third expression matrix corresponding to unique genes in single-cell data, and to construct a similarity matrix between cells based on spatial information.

[0084] The iteration module 300 is used to input the first expression matrix, the second expression matrix, the third expression matrix, and the similarity matrix into the objective function to obtain the low-dimensional representation of shared genes in the first spatial transcriptomics, the low-dimensional representation of unique genes in the first single-cell data, the low-dimensional representation of cells in the first spatial transcriptomics, and the low-dimensional representation of cells in the first single-cell data. The low-dimensional representation of shared genes in the first spatial transcriptomics, the low-dimensional representation of unique genes in the first single-cell data, the low-dimensional representation of cells in the first spatial transcriptomics, and the low-dimensional representation of cells in the first single-cell data are iteratively optimized using the objective function to obtain the low-dimensional representation of shared genes in the second spatial transcriptomics, the low-dimensional representation of unique genes in the second single-cell data, the low-dimensional representation of cells in the second spatial transcriptomics, and the low-dimensional representation of cells in the second single-cell data.

[0085] Integration module 400 is used to integrate unique gene representations from second single-cell data with low-dimensional cellular representations from second spatial transcriptomics to predict undetected gene expression.

[0086] In this embodiment, the shared genes acquired in module 100 retain the cross-modal commonalities between spatial transcriptomics data and single-cell data while also isolating unique genes from single-cell data. Various expression matrices formed by construction module 200, through the decoupling and decomposition of the first, second, and third expression matrices by iterative module 300, more realistically reflect the spatial specificity of spatial transcriptomics data. A similarity matrix transforms spatial locations into a computable form, laying the foundation for introducing spatial constraints into the subsequent objective function and ensuring that spatially adjacent cells maintain expression similarity in low-dimensional representations. This achieves synergistic preservation of undetected gene prediction and spatial heterogeneity. The integration module 400 integrates the unique gene representations of the second single-cell data with the low-dimensional cellular representations of the second spatial transcriptomics, predicting the expression of undetected genes, resulting in a more complete analysis of the molecular mechanisms of biological samples and reducing bias in disease research.

[0087] Furthermore, the iteration module 300 is also used to iteratively solve the objective function using the Lagrange multiplier method. By introducing Lagrange multipliers, the constraints are linked to the original objective function to construct a new function, thereby obtaining the values ​​of each variable when the original function reaches its extremum. The Lagrange multiplier method derives the update rules for each variable by differentiating the objective function and setting the gradient to zero. Since the objective function involves multiple variables, an alternating optimization strategy is required: fixing other variables and updating each variable one by one until the objective function converges.

[0088] Furthermore, the construction module 200 is also used to construct a similarity matrix between cells based on spatial information using a symmetric K-nearest neighbor algorithm. This transforms the spatial location information of cells in spatial transcriptomics data into computable mathematical relationships, quantifies the spatial proximity between cells, and provides a basis for introducing spatial constraints into the subsequent objective function.

[0089] This application also provides a computer-readable storage medium that stores a computer program that, when executed by a processor, implements the prediction method described above.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A spatial transcriptomics prediction method, characterized in that, The prediction method includes: Acquire spatial transcriptomics data and single-cell data, identify shared genes in the spatial transcriptomics data and the single-cell data; screen out genes that exist simultaneously in both spatial transcriptomics data and single-cell data, i.e., shared genes; Construct a first expression matrix corresponding to the shared genes in the spatial transcriptomics data, construct a second expression matrix corresponding to the shared genes in the single-cell data, and construct a third expression matrix corresponding to the unique genes in the single-cell data; A similarity matrix between cells is constructed based on spatial information. This similarity matrix is ​​then converted into a graph Laplacian matrix for use as a spatial constraint term in the subsequent objective function; including: Based on spatial information, a similarity matrix between cells is constructed using the symmetric K-nearest neighbor algorithm; The first expression matrix, the second expression matrix, the third expression matrix, and the similarity matrix are input into the objective function to obtain the low-dimensional representation of shared genes in the first spatial transcriptomics, the low-dimensional representation of unique genes in the first single-cell data, the low-dimensional representation of cells in the first spatial transcriptomics, and the low-dimensional representation of cells in the first single-cell data. The shared gene low-dimensional representations of the first spatial transcriptomics, the unique gene low-dimensional representations of the first single-cell data, the cell low-dimensional representations of the first spatial transcriptomics, and the cell low-dimensional representations of the first single-cell data are iteratively optimized using the objective function to obtain the shared gene low-dimensional representations of the second spatial transcriptomics, the unique gene low-dimensional representations of the second single-cell data, the cell low-dimensional representations of the second spatial transcriptomics, and the cell low-dimensional representations of the second single-cell data. The unique low-dimensional representation of genes from the second single-cell data is integrated with the low-dimensional cellular representation of the second spatial transcriptomics to predict the expression of undetected genes. The objective function is defined as follows: Where F is the norm, tr represents the trace of the matrix, and the first expression matrix is... The second expression matrix is The third expression matrix is , , , , For the low-dimensional representation of shared genes in first-space transcriptomics, For the low-dimensional cellular representation of first-space transcriptomics, This is a low-dimensional representation of the cells from the first single-cell data. This is a unique low-dimensional representation of genes from the first single-cell data. , , and For hyperparameters, Let T be the graph Laplacian matrix, T be the transpose of the corresponding matrix, and j represent the j-th column of the matrix. The j-th column represents the low-dimensional cellular representation of first-space transcriptomics. It is the j-th column of the low-dimensional representation of the cell in the first single-cell data.

2. The prediction method according to claim 1, characterized in that, The steps for iterative optimization using the objective function include: The objective function is solved iteratively using the Lagrange multiplier method.

3. The prediction method according to claim 2, characterized in that, The steps for iteratively solving the objective function using the Lagrange multiplier method include: The objective function is solved iteratively using the Lagrange multiplier method. The iteration terminates when the change in the objective function value is less than a preset stopping threshold, wherein the stopping threshold is in the range of 10. -5 Up to 10 -7 between.

4. The prediction method according to claim 1, characterized in that, After obtaining the shared gene low-dimensional representations of the second spatial transcriptomics, the unique gene low-dimensional representations of the second single-cell data, the cellular low-dimensional representations of the second spatial transcriptomics, and the cellular low-dimensional representations of the second single-cell data, the method further includes: Integrating the shared gene low-dimensional representations from the second spatial transcriptomics and the cellular low-dimensional representations from the second spatial transcriptomics yields denoised expression.

5. A spatial transcriptomics prediction system, characterized in that, The prediction system includes: The acquisition module is used to acquire spatial transcriptomics data and single-cell data, and to identify shared genes between the spatial transcriptomics data and the single-cell data; The construction module is used to construct a first expression matrix corresponding to the shared gene in the spatial transcriptomics data, a second expression matrix corresponding to the shared gene in the single-cell data, a third expression matrix corresponding to the unique gene in the single-cell data, and construct a similarity matrix between cells based on spatial information. The similarity matrix is ​​then converted into a graph Laplacian matrix for use as a spatial constraint term in the subsequent objective function. An iterative module is used to input the first expression matrix, the second expression matrix, the third expression matrix, and the similarity matrix into an objective function to obtain low-dimensional representations of shared genes in first spatial transcriptomics, low-dimensional representations of unique genes in first single-cell data, low-dimensional representations of cells in first spatial transcriptomics, and low-dimensional representations of cells in first single-cell data. The module then iteratively optimizes these low-dimensional representations using the objective function to obtain low-dimensional representations of shared genes in second spatial transcriptomics, low-dimensional representations of unique genes in second single-cell data, low-dimensional representations of cells in second spatial transcriptomics, and low-dimensional representations of cells in second single-cell data. An integration module is used to integrate the unique low-dimensional gene representation of the second single-cell data with the low-dimensional cellular representation of the second spatial transcriptomics to predict the expression of undetected genes. The building module is also used to construct a similarity matrix between cells based on spatial information using a symmetric K-nearest neighbor algorithm.

6. The prediction system according to claim 5, characterized in that, The iterative module is also used to iteratively solve the objective function using the Lagrange multiplier method.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the prediction method as described in any one of claims 1 to 4.

Images