WO2021142625A1 - 基于单细胞转录组测序数据预测细胞空间关系的方法 - Google Patents

基于单细胞转录组测序数据预测细胞空间关系的方法 Download PDF

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WO2021142625A1
WO2021142625A1 PCT/CN2020/072044 CN2020072044W WO2021142625A1 WO 2021142625 A1 WO2021142625 A1 WO 2021142625A1 CN 2020072044 W CN2020072044 W CN 2020072044W WO 2021142625 A1 WO2021142625 A1 WO 2021142625A1
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cell
interaction
cells
matrix
ligand
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张泽民
任仙文
钟国杰
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北京大学
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    • G—PHYSICS
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    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
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    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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    • C12N15/85—Vectors or expression systems specially adapted for eukaryotic hosts for animal cells
    • C12N15/86—Viral vectors
    • C12N15/867—Retroviral vectors

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  • the invention belongs to the field of biotechnology, and specifically relates to a method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data.
  • the spatial structure of cells is crucial for understanding the behavior and function of cells. How to map the spatial organization of cells in tissues and organs is an important proposition in the field of biomedicine.
  • the method of mapping the spatial organization of cells is based on experiments, using fluorescence or other methods to label important genes, proteins or other biological molecules, and then image them through a microscope to finally obtain the spatial distribution information of the cells.
  • the marker genes related to the spatial position of the cell can be determined according to the aforementioned experimental method, and then the marker gene with the determined spatial position is combined with the single-cell transcriptome sequencing data to map the cells with the transcriptome sequencing data to the Known cell space image.
  • the ligand-receptor interaction plays an important role in cell interaction and communication.
  • the ligand-receptor cell interaction and cell spatial structure at the individual cell level have not been found Refactoring.
  • an embodiment of the present invention proposes a method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data, including:
  • model for reconstructing the three-dimensional structure of cell interaction is:
  • p ij is the interaction intensity of cell i and cell j in the probability matrix P of the cell-cell interaction intensity matrix A,
  • q ij is the probability that cell j is around cell i
  • d ij is the Euclidean distance between cell i and cell j in the three-dimensional space
  • C is the objective function
  • y i is the current coordinate of cell i in one dimension
  • y j is the current coordinate of cell j in this dimension
  • the cell-cell interaction strength matrix A is obtained, and each element of the cell-cell interaction strength matrix A is divided by the cell-cell The sum of all elements Z p in the interaction strength matrix A, to obtain the probability matrix P of the cell-cell interaction strength matrix A,
  • I is the total number of cells
  • K is the total number of ligand-receptor pairs
  • the elements in the probability matrix P of the cell-cell interaction strength matrix A are:
  • each element in the cell-cell interaction strength matrix A is the corresponding interaction strength between the cell C1 and the cell C2, and the relationship formula of the interaction strength is:
  • a C1, C2 represent the cell-cell interaction strength between cell C1 and cell C2,
  • w A, B represents the weight of the interaction between ligand A and receptor B
  • a C1 and A C2 represent the expression level of ligand A in cell C1 and cell C2, respectively,
  • B C1 and B C2 represent the expression level of receptor B in cell C1 and cell C2, respectively.
  • K represents the total number of ligand-receptor pairs.
  • the average cell-to-cell distance threshold for interaction between each cell and h cells is determined by the following method:
  • the distance to the cell close to the h-th order is determined, and the median of the determined distance values for all cells is calculated to obtain the average inter-cell distance threshold value for each cell interacting with h cells.
  • the obtained probability matrix P of the cell-cell interaction strength matrix A is discretized.
  • the expression levels of the ligands and receptors are measured by TPM, FPKM, CPM, Counts, TP10K, log2 (TPM+1).
  • the method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data proposed in the embodiments of the present invention can predict the interaction of cells in three-dimensional space only by using single-cell transcriptome sequencing data, which solves the existing problems.
  • imaging must be used to obtain the limitations of the spatial relationship of cells.
  • the predicted cellular spatial relationships can be used to analyze related molecular mechanisms, molecular effects, cellular spatial categories, individual response to treatment, or the utility of different treatment methods.
  • evaluating the statistical significance of cell-cell interactions based on the reconstructed cell space structure scoring ligand-receptor pairs for cell-cell interactions or cell-cell interactions; simulating genes by computer Knockout, overexpression, cell adoptive input, cell censorship and other interference experiments to evaluate the influence of a certain gene or cell on the cell space structure; cell clustering based on the reconstructed cell space structure; analysis based on the space structure Differentially expressed genes of defined cell types, looking for genes related to cell therapy or immunotherapy response or resistance; based on the reconstructed cell spatial structure information, infer patients or disease types with good or poor response to cell therapy or immunotherapy.
  • FIG. 1 is a flowchart of a method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data according to an embodiment of the present invention
  • [Corrected according to Rule 91 10.03.2020] 2 is a flowchart of a method for predicting spatial relationships of cells based on single-cell transcriptome sequencing data according to another embodiment of the present invention
  • FIG. 3 is a flowchart of a method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data in an example of the present invention
  • FIG. 4 is a distribution diagram of all cells in an initialized three-dimensional coordinate system in the method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data according to an embodiment of the present invention
  • Fig. 5 is a schematic diagram of the cell coordinate update process in the method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data according to an embodiment of the present invention.
  • an embodiment of the present invention proposes a method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data, which includes the following steps:
  • the embodiment of the present invention proposes a method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data.
  • the core of the method is to calculate the cell-cell interaction strength matrix based on the single-cell transcriptome sequencing data, and to calculate the cell-cell interaction strength matrix in the first step.
  • -Cell interaction strength matrix reconstructs the three-dimensional structure of cell interaction, as shown in Figure 1, including:
  • Step S1 Obtain the cell-cell interaction strength matrix A based on the single-cell transcriptome sequencing data and the public receptor-ligand database;
  • the gene expression matrix E is obtained.
  • the public receptor-ligand database such as CellphoneDB
  • the cell-cell interaction strength between two cells can be calculated, and the cell-cell between two cells-
  • the relational formula of cell interaction strength is expressed as:
  • a C1, C2 represent the strength of cell-cell interaction between cell C1 and cell C2
  • w A, B represent the weight of the interaction between ligand A and receptor B
  • a C1 and A C2 represent ligands, respectively
  • B C1 and B C2 represent the expression level of receptor B in cell C1 and cell C2, respectively
  • K represents the total number of ligand-receptor pairs.
  • the default value of w A, B is 1, which can be replaced according to the chemical or other properties of the ligand-receptor pair.
  • the expression levels of ligands and receptors can be measured by various methods such as TPM, FPKM, CPM, Counts, TP10K, log2(TPM+1), etc.
  • TPM transcription per million
  • the A C1 and C2 obtained by the above calculation are subjected to monotonic transformation, such as exponential transformation, logarithmic transformation, power law transformation, and the like.
  • the cell-cell interaction strength matrix A After obtaining the cell-cell interaction strength of all cell pairs, the cell-cell interaction strength matrix A can be obtained. Each element in the cell-cell interaction strength matrix A is the corresponding cell C1 and cell C2.
  • the interaction strength of the interaction strength has the above-mentioned relational formula.
  • Step S2 Normalize the cell-cell interaction strength matrix A, and divide each element of the cell-cell interaction strength matrix A by the sum of all elements Z p in the cell-cell interaction strength matrix A to obtain the cell-cell
  • the probability matrix P of the interaction strength matrix A, the elements in the probability matrix P are:
  • p ij is the interaction intensity of cell i and cell j in the probability matrix P of the cell-cell interaction intensity matrix A;
  • K is the total number of ligand-receptor pairs
  • Is the k-th ligand-receptor chemical binding constant the default is 1, or it can be an experimentally determined value
  • Step S3 According to the obtained probability matrix P of the cell-cell interaction strength matrix A, reconstruct the three-dimensional structure of the cell interaction, and the model of the three-dimensional structure of the reconstructed cell interaction is:
  • the objective function is defined by the Kullback-Leibler divergence, such that:
  • I is the total number of cells
  • q ij is the probability that cell j is around cell i
  • d ij is the Euclidean distance between cell i and cell j in the three-dimensional space
  • r is the minimum distance between two cells
  • R is the size of the radius of the three-dimensional space, and R is much larger than r.
  • the objective function is defined by the Kullback-Leibler divergence, and the definitions of p ij , q ij and di ij are given, and the steric hindrance effect is expressed by an inequality.
  • Step S4 For each cell in the three-dimensional structure of the reconstructed cell interaction, select the average cell-to-cell distance threshold at which each cell interacts with h cells, so that each cell interacts with h cells on average to obtain a cell Interaction network.
  • h is the number of cells interacting with the current cell, which can be selected by those skilled in the art according to the situation, for example, h is 3, 5, or 10, etc.
  • the distance to the cell close to the h-th order is calculated, and the median of the distance values calculated for all cells is calculated to obtain the average inter-cell distance threshold value of interaction between each cell and h cells.
  • the inter-cell distance threshold for each pair of cells, if their distance is less than the threshold, they are considered to have an interaction; if their distance is greater than the threshold, then they are considered to have no interaction, thus obtaining the cell mutual Function network.
  • the method for predicting the spatial relationship of cells based on single-cell transcriptome sequencing data includes the following steps:
  • Step S10 Based on the single-cell transcriptome sequencing data, the cell-cell interaction strength matrix A is obtained according to the public receptor-ligand database.
  • the expression level of ligand and receptor can be measured by TPM.
  • the receptor-ligand TPM value data of each single cell can be read. , And then obtain the cell-cell interaction strength matrix A.
  • Step S20 Normalize the cell-cell interaction strength matrix A, and divide each element of the cell-cell interaction strength matrix A by the sum of all elements Z p in the cell-cell interaction strength matrix A to obtain the cell-cell
  • the probability matrix P of the interaction strength matrix A, the elements in the probability matrix P are:
  • Step S30 Discretize the probability matrix P of the cell-cell interaction strength matrix.
  • the probability matrix P of the cell-cell interaction strength matrix is discretized. Usually select the largest first 50 elements in each row or column.
  • this step is an optional step, and it is feasible without this step.
  • Step S40 In the three-dimensional space, randomly initialize the coordinates of all cells.
  • Step S50 According to the obtained probability matrix P of the cell-cell interaction strength matrix A, reconstruct the three-dimensional structure of the cell interaction, and the model of the three-dimensional structure of the reconstructed cell interaction is:
  • Step S60 For each cell in the three-dimensional structure of the reconstructed cell interaction, select the average cell-to-cell distance threshold at which each cell interacts with h cells, so that each cell interacts with h cells on average to obtain a cell Interaction network.
  • the cell-cell interaction strength matrix A is obtained, and then the probability matrix P of the cell-cell interaction strength matrix A is obtained.
  • the expression level of ligand and receptor can be measured by TPM.
  • the coordinates of all cells are initialized randomly.
  • the distribution map of all cells in the initialized three-dimensional coordinate system is shown in Figure 4, where B-cell is B-cell, CAF is cancer-related fibroblast, and Endothelial is endothelial Cells, Macrophage are macrophages, NK are natural killer cells, T-cells are T cells, Malignant are tumor cells, and Normal are normal cells.
  • C is the objective function
  • y i is the current coordinate of cell i in a certain dimension
  • y j is the current coordinate of cell j in this dimension.
  • FIG. 5 shows a schematic diagram of the cells in the three-dimensional coordinate system when iterating 200 times, 400 times, 600 times, 800 times, and 1000 times.
  • each cell in the three-dimensional structure of the reconstructed cell interaction select the average cell-to-cell distance threshold at which each cell interacts with 3 cells, so that each cell interacts with 3 cells on average to obtain the intercellular interaction network .

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Abstract

一种基于单细胞转录组测序数据预测细胞空间关系的方法，包括：获取基于单细胞转录组测序数据的细胞-细胞相互作用强度矩阵A的概率矩阵P；根据获取的所述细胞-细胞相互作用强度矩阵A的概率矩阵P，重构细胞相互作用的三维空间结构；对于重构细胞相互作用的三维空间结构中的每个细胞，确定平均每个细胞与h个细胞相互作用的细胞间距离阈值，得到细胞间作用网络。本方法只需要单细胞转录组测序数据就可以预测细胞在三维空间中的相互作用，解决了现有技术中必须通过成像才能获得细胞空间关系的限制。

Description

基于单细胞转录组测序数据预测细胞空间关系的方法 技术领域
本发明属于生物技术领域，具体涉及一种基于单细胞转录组测序数据预测细胞空间关系的方法。
背景技术
细胞空间结构对于理解细胞的行为和功能具有至关重要的作用，如何测绘细胞在组织、器官中的空间组织形式是生物医学领域的重要命题。
目前，测绘细胞空间组织方式的办法是以实验为基础，通过荧光或其他方法对重要的基因、蛋白或其他生物分子进行标记，然后通过显微镜成像，最终获得细胞的空间分布信息。已有的计算方法中，可以根据前述实验方法确定出与细胞空间位置相关的标记基因，进而利用确定空间位置的标记基因结合单细胞转录组测序数据，将具有转录组测序数据的细胞映射到已知的细胞空间图像上。现有技术中还没有计算方法可以不依赖已知的细胞空间图像、只利用单细胞转录组测序数据对细胞空间结构进行重构。
此外，配体-受体相互作用在细胞相互作用和通讯中发挥着重要作用，在已有的计算方法中，存在根据单细胞转录组测序数据来衡量细胞类和细胞类之间某种配体-受体对的相互作用或配体-受体对的个数是否显著强于其他细胞类对，但是，还未发现根据配体-受体进行单个细胞级别的细胞相互作用和细胞空间结构的重构。
发明内容
为解决上述问题，本发明实施例提出了一种基于单细胞转录组测序数据预测细胞空间关系的方法，包括：
获取基于单细胞转录组测序数据的细胞-细胞相互作用强度矩阵A的概率矩阵P；
根据获取的所述细胞-细胞相互作用强度矩阵A的概率矩阵P，重构细胞相互作用的三维空间结构；
对于重构细胞相互作用的三维空间结构中的每个细胞，确定平均每个细胞与h个细胞相互作用的细胞间距离阈值，得到细胞间作用网络。
进一步，重构细胞相互作用的三维空间结构的模型为：
最小化目标函数
Figure PCTCN2020072044-appb-000001
使得：
Figure PCTCN2020072044-appb-000002
Figure PCTCN2020072044-appb-000003
Figure PCTCN2020072044-appb-000004
其中，I是细胞的总数，
p ij是所述细胞-细胞相互作用强度矩阵A的概率矩阵P中细胞i与细胞j的作用强度，
q ij是细胞j在细胞i周围的概率，
d ij是细胞i与细胞j在三维空间中的欧几里得距离，
Figure PCTCN2020072044-appb-000005
是细胞i的第m维的坐标值，
Figure PCTCN2020072044-appb-000006
是细胞j的第m维的坐标值；
进一步，最小化目标函数
Figure PCTCN2020072044-appb-000007
采用梯度下降 法更新细胞坐标，计算当前坐标下每个细胞的梯度方向：
Figure PCTCN2020072044-appb-000008
其中，C为目标函数，y i为细胞i在一维度上的当前坐标，y j为细胞j在该维度上的当前坐标，
以该梯度方向为坐标更新方向，以固定步长更新细胞坐标，进行多次迭代。
进一步，当细胞i与细胞j的距离小于三维空间中两个细胞间的最小距离r时，若p ij-q ij>0，则令p ij-q ij＝s，s为不小于-1的负数。
进一步，基于单细胞转录组测序数据，根据公开的受体-配体数据库，得到细胞-细胞相互作用强度矩阵A，将所述细胞-细胞相互作用强度矩阵A的每个元素除以细胞-细胞相互作用强度矩阵A中所有元素之和Z p，得到所述细胞-细胞相互作用强度矩阵A的概率矩阵P，
Figure PCTCN2020072044-appb-000009
其中：
I是细胞的总数；
K是配体-受体对的总数；
Figure PCTCN2020072044-appb-000010
是表示第k对配体-受体的化学结合常数；
Figure PCTCN2020072044-appb-000011
是第k个配体在细胞i中的表达水平；
Figure PCTCN2020072044-appb-000012
是第k个受体在细胞i中的表达水平；
Figure PCTCN2020072044-appb-000013
是第k个配体在细胞j中的表达水平；
Figure PCTCN2020072044-appb-000014
是第k个受体在细胞j中的表达水平。
进一步，所述细胞-细胞相互作用强度矩阵A的概率矩阵P中的元素为：
Figure PCTCN2020072044-appb-000015
进一步，所述细胞-细胞相互作用强度矩阵A中的每个元素为对应 的细胞C1与细胞C2之间的相互作用强度，所述相互作用强度的关系式为：
Figure PCTCN2020072044-appb-000016
或者
Figure PCTCN2020072044-appb-000017
或者
Figure PCTCN2020072044-appb-000018
其中，A C1,C2表示细胞C1和细胞C2之间的细胞-细胞相互作用强度，
w A,B表示配体A和受体B之间相互作用的权重，
A C1和A C2分别表示配体A在细胞C1和细胞C2中的表达水平，
B C1和B C2分别表示受体B在细胞C1和细胞C2中的表达水平，
K表示配体-受体对的总数。
进一步，所述平均每个细胞与h个细胞相互作用的细胞间距离阈值采用如下方法确定：
对于每一个细胞，均确定与与其第h次序接近的细胞的距离，对所有细胞确定的所述距离值求中位数，获得平均每个细胞与h个细胞相互作用的细胞间距离阈值。
进一步，在重构细胞相互作用的三维空间结构之前，对获取的所述细胞-细胞相互作用强度矩阵A的概率矩阵P进行离散化处理。
进一步，所述配体和受体表达水平采用TPM、FPKM、CPM、Counts、TP10K、log2(TPM+1)计量。
本发明的有益效果：本发明实施例提出的基于单细胞转录组测序数据预测细胞空间关系的方法，只需要单细胞转录组测序数据就可以预测细胞在三维空间中的相互作用，解决了现有技术中必须通过成像才能获 得细胞空间关系的限制。预测得到的细胞空间关系能够用于分析相关的分子机制、分子效应、细胞空间类别、个体对治疗的响应或不同治疗方法的效用等。例如，根据重构的细胞空间结构评价细胞类-细胞类相互作用统计显著性；对细胞-细胞相互作用或细胞类-细胞类相互作用的配体-受体对的打分方法；通过计算机模拟基因敲除、过表达、细胞过继性输入、细胞删失等干扰实验，评价某个或某些基因或细胞对细胞空间结构影响；基于重构的细胞空间结构对细胞聚类；通过分析基于空间结构定义的细胞类的差异表达基因，寻找与细胞治疗或免疫治疗响应或抵抗有关的基因；基于重构的细胞空间结构信息，推断对细胞治疗或免疫治疗响应良好或较差的病人或病种。
附图说明
图1是本发明实施例提出的基于单细胞转录组测序数据预测细胞空间关系的方法的流程图；
[根据细则91更正 10.03.2020]　
图2是本发明又一实施例提出的基于单细胞转录组测序数据预测细胞空间关系的方法的流程图；
图3是本发明的一个示例中的基于单细胞转录组测序数据预测细胞空间关系的方法的流程图；
图4是本发明实施例提出的基于单细胞转录组测序数据预测细胞空间关系的方法中，所有细胞在初始化后的三维坐标系中的分布图；
图5是本发明实施例提出的基于单细胞转录组测序数据预测细胞空间关系的方法中，细胞坐标更新过程示意图。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚明白，以下结合具体 实施例，并参照附图，对本发明进一步详细说明。但本领域技术人员知晓，本发明并不局限于附图和以下实施例。
本发明的发明人认为由配体-受体对介导的细胞相互作用在细胞空间结构形成中发挥重要作用，相互作用的细胞通过竞争空间位置形成了空间结构。在此基础上，本发明实施例提出了一种基于单细胞转录组测序数据预测细胞空间关系的方法，包括如下步骤：
本发明实施例提出一种基于单细胞转录组测序数据预测细胞空间关系的方法，其核心在于，根据单细胞转录组测序数据计算细胞-细胞相互作用强度矩阵，并根据第一步计算得到的细胞-细胞相互作用强度矩阵重构细胞相互作用的三维空间结构，如图1所示，包括：
步骤S1：基于单细胞转录组测序数据，根据公开的受体-配体数据库，得到细胞-细胞相互作用强度矩阵A；
根据单细胞转录组测序数据得到基因表达矩阵E，根据公开的受体-配体数据库，例如CellphoneDB，能够计算得到两个细胞之间的细胞-细胞相互作用强度，两个细胞之间的细胞-细胞相互作用强度的关系式根据化学反应中的质量作用定律(Law of mass action)表示为：
Figure PCTCN2020072044-appb-000019
或者
Figure PCTCN2020072044-appb-000020
或者
Figure PCTCN2020072044-appb-000021
其中，A C1,C2表示细胞C1和细胞C2之间的细胞-细胞相互作用强度，w A,B表示配体A和受体B之间相互作用的权重，A C1和A C2分别表示配体A在细胞C1和细胞C2中的表达水平，B C1和B C2分别表示受体B在细胞C1和细胞C2中的表达水平，K表示配体-受体对的总数。w A,B的默 认值为1，可以根据配体-受体对的化学或其他性质进行相应替换。
在该公式中，配体和受体表达水平的计量可以采用如TPM、FPKM、CPM、Counts、TP10K、log2(TPM+1)等多种方法。当例如采用TPM(transcripts per million)计量时，上述两个细胞之间的细胞-细胞相互作用强度的计算公式表示为：
Figure PCTCN2020072044-appb-000022
或者
Figure PCTCN2020072044-appb-000023
或者
Figure PCTCN2020072044-appb-000024
在本发明的优选方式中，对上述计算得到的A C1,C2进行单调变换，如指数变换、对数变换、幂律变换等。
在得到所有细胞对的细胞-细胞相互作用强度以后，可以得到细胞-细胞相互作用强度矩阵A，所述细胞-细胞相互作用强度矩阵A中的每个元素为对应的细胞C1与细胞C2之间的相互作用强度，所述相互作用强度具有上述关系式。
步骤S2：对细胞-细胞相互作用强度矩阵A进行标准化，将细胞-细胞相互作用强度矩阵A的每个元素除以细胞-细胞相互作用强度矩阵A中所有元素之和Z p，得到细胞-细胞相互作用强度矩阵A的概率矩阵P，所述概率矩阵P中的元素为：
Figure PCTCN2020072044-appb-000025
Figure PCTCN2020072044-appb-000026
其中，p ij是所述细胞-细胞相互作用强度矩阵A的概率矩阵P中细胞i与细胞j的作用强度；
K是配体-受体对的总数；
Figure PCTCN2020072044-appb-000027
是表示第k对配体-受体的化学结合常数，默认为1，也可以是实验测定的数值；
Figure PCTCN2020072044-appb-000028
是第k个配体在细胞i中的表达水平；
Figure PCTCN2020072044-appb-000029
是第k个受体在细胞i中的表达水平；
Figure PCTCN2020072044-appb-000030
是第k个配体在细胞j中的表达水平；
Figure PCTCN2020072044-appb-000031
是第k个受体在细胞j中的表达水平。
步骤S3：根据得到的所述细胞-细胞相互作用强度矩阵A的概率矩阵P，重构细胞相互作用的三维空间结构，所述重构细胞相互作用的三维空间结构的模型为：
最小化目标函数
Figure PCTCN2020072044-appb-000032
目标函数由Kullback-Leibler散度所定义，使得：
Figure PCTCN2020072044-appb-000033
Figure PCTCN2020072044-appb-000034
Figure PCTCN2020072044-appb-000035
d ij≥r for i≠j
Figure PCTCN2020072044-appb-000036
其中，I是细胞的总数；
q ij是细胞j在细胞i周围的概率；
d ij是细胞i与细胞j在三维空间中的欧几里得距离；
Figure PCTCN2020072044-appb-000037
是细胞i的第m维的坐标值；
Figure PCTCN2020072044-appb-000038
是细胞j的第m维的坐标值；
r是两个细胞间的最小距离；
R是三维空间半径的大小，R远大于r。
在上述公式中，目标函数由Kullback-Leibler散度所定义，且给出了p ij、q ij和d ij的定义，并通过不等式表示了空间位阻效应。
步骤S4：对于重构细胞相互作用的三维空间结构中的每个细胞，选取平均每个细胞与h个细胞相互作用的细胞间距离阈值，使得平均每个细胞与h个细胞相互作用，得到细胞间作用网络。
具体的，其中的h为与当前细胞相互作用的细胞个数，本领域技术人员可以根据情况进行选择，如h为3、5或10等。对于每一个细胞，均计算与与其第h次序接近的细胞的距离，对所有细胞计算的所述距离值求中位数，获得平均每个细胞与h个细胞相互作用的细胞间距离阈值。获得细胞间距离阈值后，对于每对细胞，如果它们的距离小于所述阈值，则认为它们存在相互作用；如果它们的距离大于阈值，则认为它们之间不存在相互作用，从而获得了细胞相互作用网络。
在本发明的一个具体实施例中，如图2所示，所述基于单细胞转录组测序数据预测细胞空间关系的方法包括如下步骤：
步骤S10：基于单细胞转录组测序数据，根据公开的受体-配体数据库，得到细胞-细胞相互作用强度矩阵A。
在本发明的实施例中，如前所述，配体和受体表达水平可以采用TPM计量，根据公开的受体-配体数据库，读取每个单细胞的受体-配体TPM值数据，进而得到细胞-细胞相互作用强度矩阵A。
步骤S20：对细胞-细胞相互作用强度矩阵A进行标准化，将细胞-细胞相互作用强度矩阵A的每个元素除以细胞-细胞相互作用强度矩阵A中所有元素之和Z p，得到细胞-细胞相互作用强度矩阵A的概率矩阵P，所述概率矩阵P中的元素为：
Figure PCTCN2020072044-appb-000039
步骤S30：离散化所述细胞-细胞相互作用强度矩阵的概率矩阵P。
在本发明优选实施例中，对所述细胞-细胞相互作用强度矩阵的概率矩阵P进行离散化处理。通常在每行或每列中选取最大的前50个元素即可。
本领域技术人员可以理解，此步骤是可选择的步骤，没有此步骤也是可行的。
步骤S40：在三维空间中，随机初始化所有细胞的坐标。
在三维空间中，随机以一个细胞的位置做为原点，为其他细胞确定坐标。
步骤S50：根据得到的所述细胞-细胞相互作用强度矩阵A的概率矩阵P，重构细胞相互作用的三维空间结构，所述重构细胞相互作用的三维空间结构的模型为：
最小化目标函数
Figure PCTCN2020072044-appb-000040
步骤S60：对于重构细胞相互作用的三维空间结构中的每个细胞，选取平均每个细胞与h个细胞相互作用的细胞间距离阈值，使得平均每个细胞与h个细胞相互作用，得到细胞间作用网络。
以下，以取用melanoma数据库中的5000个细胞的单细胞转录组数据为例，说明本发明的预测细胞空间关系的方法，如图3所示。
基于单细胞转录组测序数据，根据公开的受体-配体数据库，得到细胞-细胞相互作用强度矩阵A，进而得到细胞-细胞相互作用强度矩阵A的概率矩阵P，在本发明的实施例中，配体和受体表达水平可以采用TPM计量。
离散化所述细胞-细胞相互作用强度矩阵的概率矩阵P,保留矩阵每行最大的50个元素。
在50x50x50的三维空间中，随机初始化所有细胞的坐标。在本实施 例的melanoma数据库的条件下，所有细胞在初始化后的三维坐标系中的分布图如图4所示，其中，B-cell为B细胞，CAF为癌症相关成纤维细胞，Endothelial为内皮细胞，Macrophage为巨噬细胞，NK为自然杀伤细胞，T-cell为T细胞，Malignant为肿瘤细胞，Normal为正常细胞。
最小化目标函数
Figure PCTCN2020072044-appb-000041
采用梯度下降法更新细胞坐标。
计算当前坐标下每个细胞的梯度方向：
Figure PCTCN2020072044-appb-000042
其中，C为目标函数，y i为细胞i在某一维度上的当前坐标，y j为细胞j在该维度上的当前坐标。以该梯度方向为坐标更新方向，以固定步长更新细胞坐标，进行多次迭代，总共迭代1000-2000次，本实施例中进行1000次迭代。
考虑到空间位阻效应，
d ij≥r for i≠j，
Figure PCTCN2020072044-appb-000043
在本实施例中，r＝0.01，R＝50。当细胞i与细胞j的距离小于r＝0.01时，若上述公式中的p ij-q ij>0，则使得p ij-q ij＝s，s为不小于-1的负数。当迭代过程中出现细胞的坐标值大于R＝50时，将所有细胞的坐标同比例缩小，使得所有细胞的坐标值仍然小于R＝50。
本步骤中的细胞坐标更新过程如图5所示，图5中示出了迭代200次、400次、600次、800次和1000次时细胞在三维坐标系中的示意图。
对于重构细胞相互作用的三维空间结构中的每个细胞，选取平均每个细胞与3个细胞相互作用的细胞间距离阈值，使得平均每个细胞与3个细胞相互作用，得到细胞间作用网络。
在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或 示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。
以上，对本发明的实施方式进行了说明。但是，本发明不限定于上述实施方式。凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种基于单细胞转录组测序数据预测细胞空间关系的方法，其特征在于，所述方法包括：
    获取基于单细胞转录组测序数据的细胞-细胞相互作用强度矩阵A的概率矩阵P；
    根据获取的所述细胞-细胞相互作用强度矩阵A的概率矩阵P，重构细胞相互作用的三维空间结构；
    对于重构细胞相互作用的三维空间结构中的每个细胞，确定平均每个细胞与h个细胞相互作用的细胞间距离阈值，得到细胞间作用网络。
  2. 如权利要求1所述的方法，其特征在于，重构细胞相互作用的三维空间结构的模型为：
    最小化目标函数
    Figure PCTCN2020072044-appb-100001
    使得：
    Figure PCTCN2020072044-appb-100002
    Figure PCTCN2020072044-appb-100003
    Figure PCTCN2020072044-appb-100004
    其中，I是细胞的总数，
    p ij是所述细胞-细胞相互作用强度矩阵A的概率矩阵P中细胞i与细胞j的作用强度，
    q ij是细胞j在细胞i周围的概率，
    d ij是细胞i与细胞j在三维空间中的欧几里得距离，
    Figure PCTCN2020072044-appb-100005
    是细胞i的第m维的坐标值，
    Figure PCTCN2020072044-appb-100006
    是细胞j的第m维的坐标值；
  3. 如权利要求2所述的方法，其特征在于，最小化目标函数
    Figure PCTCN2020072044-appb-100007
    采用梯度下降法更新细胞坐标，计算当前坐标下每个细胞的梯度方向：
    Figure PCTCN2020072044-appb-100008
    其中，C为目标函数，y i为细胞i在一维度上的当前坐标，y j为细胞j在该维度上的当前坐标，
    以该梯度方向为坐标更新方向，以固定步长更新细胞坐标，进行多次迭代。
  4. 如权利要求3所述的方法，其特征在于，当细胞i与细胞j的距离小于三维空间中两个细胞间的最小距离r时，若p ij-q ij>0，则令p ij-q ij＝s，s为不小于-1的负数。
  5. 如权利要求1所述的方法，其特征在于，基于单细胞转录组测序数据，根据公开的受体-配体数据库，得到细胞-细胞相互作用强度矩阵A，将所述细胞-细胞相互作用强度矩阵A的每个元素除以细胞-细胞相互作用强度矩阵A中所有元素之和Z p，得到所述细胞-细胞相互作用强度矩阵A的概率矩阵P，
    Figure PCTCN2020072044-appb-100009
    其中：
    I是细胞的总数；
    K是配体-受体对的总数；
    Figure PCTCN2020072044-appb-100010
    是表示第k对配体-受体的化学结合常数；
    Figure PCTCN2020072044-appb-100011
    是第k个配体在细胞i中的表达水平；
    Figure PCTCN2020072044-appb-100012
    是第k个受体在细胞i中的表达水平；
    Figure PCTCN2020072044-appb-100013
    是第k个配体在细胞j中的表达水平；
    Figure PCTCN2020072044-appb-100014
    是第k个受体在细胞j中的表达水平。
  6. 如权利要求5所述的方法，其特征在于，所述细胞-细胞相互作用强度矩阵A的概率矩阵P中的元素为：
    Figure PCTCN2020072044-appb-100015
  7. 如权利要求1所述的方法，其特征在于，所述细胞-细胞相互作用强度矩阵A中的每个元素为对应的细胞C1与细胞C2之间的相互作用强度，所述相互作用强度的关系式为：
    Figure PCTCN2020072044-appb-100016
    或者
    Figure PCTCN2020072044-appb-100017
    或者
    Figure PCTCN2020072044-appb-100018
    其中，A C1,C2表示细胞C1和细胞C2之间的细胞-细胞相互作用强度，
    w A,B表示配体A和受体B之间相互作用的权重，
    A C1和A C2分别表示配体A在细胞C1和细胞C2中的表达水平，
    B C1和B C2分别表示受体B在细胞C1和细胞C2中的表达水平，
    K表示配体-受体对的总数。
  8. 如权利要求1所述的方法，其特征在于，所述平均每个细胞与h个细胞相互作用的细胞间距离阈值采用如下方法确定：
    对于每一个细胞，均确定与与其第h次序接近的细胞的距离，对所有细胞确定的所述距离值求中位数，获得平均每个细胞与h个细胞相互作用的细胞间距离阈值。
  9. 如权利要求1所述的方法，其特征在于，在重构细胞相互作用的三维空间结构之前，对获取的所述细胞-细胞相互作用强度矩阵A的概率矩阵P进行离散化处理。
  10. 如权利要求5或7所述的方法，其特征在于，所述配体和受体表达水平采用TPM、FPKM、CPM、Counts、TP10K、log2(TPM+1)计量。
PCT/CN2020/072044 2020-01-14 2020-01-14 基于单细胞转录组测序数据预测细胞空间关系的方法 WO2021142625A1 (zh)

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