Single-cell developmental trajectory reconstruction method, device, electronic device and storage medium

Abstract

The present invention provides a method, device, electronic device and storage medium for reconstructing the developmental trajectory of a single cell, which relates to the field of computer technology. The method includes: generating a gene regulatory network corresponding to the single cell based on a gene data set of the single cell; determining a differential equation corresponding to the gene regulatory network based on the gene regulatory network; determining a probability distribution corresponding to the gene regulatory network based on the differential equation; and establishing a potential energy topography map of the single cell based on the probability distribution. Through the above method, a nonlinear differential equation for reconstructing the developmental trajectory of a single cell is determined based on the gene regulatory network, and a probability distribution corresponding to the gene regulatory network is determined based on the differential equation. Based on the probability distribution, the developmental state of each cell of the single cell can be arranged in chronological order on the corresponding trajectory, thereby generating an intuitive potential energy topography map for reflecting the developmental trajectory of the single cell, thereby reconstructing the differentiation and developmental trajectory of the single cell in the tissue.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a method, device, electronic device and storage medium for reconstructing the developmental trajectory of a single cell. Background Art

[0002] With the rapid development of single-cell sequencing technology and the emergence of a large number of corresponding analysis tools, the application of single-cell sequencing has gradually matured, and the biological problems it can solve are becoming more and more extensive. Single-cell transcriptome sequencing can study the function and phenotype of cells at the individual cell level.

[0003] However, in related technologies, after a sample is subjected to single-cell transcriptome sequencing, the cell has already died, making it impossible to track subsequent changes in the cell. Cell trajectory analysis can reconstruct the changes in cells over time by constructing the trajectories of changes between cells, helping people infer the evolution and differentiation processes between cells at the single-cell level.

[0004] Therefore, how to reconstruct the developmental trajectory of single cells is an urgent problem to be solved. Summary of the Invention

[0005] In response to the problems existing in the prior art, embodiments of the present invention provide a method, device, electronic device, and storage medium for reconstructing the developmental trajectory of a single cell.

[0006] The present invention provides a method for reconstructing the developmental trajectory of a single cell, comprising:

[0007] Based on the gene dataset of a single cell, generating a gene regulatory network corresponding to the single cell;

[0008] Based on the gene regulatory network, determining a differential equation corresponding to the gene regulatory network, wherein the differential equation is used to reconstruct the developmental trajectory of the single cell;

[0009] Based on the differential equation, determining a probability distribution corresponding to the gene regulatory network; the probability distribution is used to assist in establishing a potential energy topography map of the single cell;

[0010] Based on the probability distribution, the potential energy landform map is established, wherein the minimum transition path in the potential energy landform map is used to reflect the developmental trajectory of the single cell.

[0011] Optionally, generating a gene regulatory network corresponding to a single cell based on a single cell gene dataset includes:

[0012] In a case where the gene regulatory network is a time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset;

[0013] The adjustable parameters of the initial gene regulatory network are optimized using a least squares algorithm to generate a gene regulatory network corresponding to the single cell.

[0014] Optionally, generating a gene regulatory network corresponding to a single cell based on a single cell gene dataset includes:

[0015] In a case where the gene regulatory network is a non-time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset;

[0016] Based on the steady-state data of gene expression corresponding to the single cell, the adjustable parameters of the initial gene regulatory network are optimized using a target algorithm to generate the gene regulatory network corresponding to the single cell; the target algorithm includes at least one of the following: a random parameter search algorithm, a particle swarm algorithm, and a gradient descent algorithm.

[0017] Optionally, the steady-state data is determined by:

[0018] performing Perron clustering on the ratio between the abundance of precursor messenger RNA (mRNA) and mature mRNA of the single cell and the cytoplasmic small RNA count matrix to determine a global fate map of the single cell, wherein the global fate map includes at least one cell state of the single cell, and the cell state includes an initial cell state, an intermediate cell state, and a terminal cell state;

[0019] The steady-state data is determined based on the global fate map and the probability of the single cell reaching each cell state.

[0020] Optionally, determining the potential energy topography of the single cell based on the probability distribution includes:

[0021] Based on the probability distribution, determining a potential function, wherein the potential function is used to construct a potential energy topography map of the single cell;

[0022] Based on the potential function, a minimum transition path algorithm is used to determine the potential energy topography of the single cell.

[0023] Optionally, after determining the potential energy topography of the single cell, the method further comprises:

[0024] determining all equilibrium points of the potential energy topography map based on the steady-state data;

[0025] According to Lyapunov's stability theory, all steady states in each equilibrium point are determined, and the potential energy topography map is updated.

[0026] The present invention also provides a single-cell developmental trajectory reconstruction device, comprising:

[0027] A generation module, configured to generate a gene regulatory network corresponding to a single cell based on a gene dataset of the single cell;

[0028] A first determination module is configured to determine a differential equation corresponding to the gene regulatory network based on the gene regulatory network, wherein the differential equation is used to reconstruct the developmental trajectory of the single cell;

[0029] A second determination module is configured to determine a probability distribution corresponding to the gene regulatory network based on the differential equation; the probability distribution is used to assist in establishing a potential energy topography map of the single cell;

[0030] An establishment module is used to establish the potential energy landform map based on the probability distribution, wherein the minimum transition path in the potential energy landform map is used to reflect the development trajectory of the single cell.

[0031] The present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a method for reconstructing the developmental trajectory of a single cell as described above is implemented.

[0032] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-described methods for reconstructing the developmental trajectory of a single cell.

[0033] The present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-described methods for reconstructing the developmental trajectory of a single cell.

[0034] The single-cell developmental trajectory reconstruction method, device, electronic device and storage medium provided by the present invention generate a gene regulatory network corresponding to the single cell based on the single-cell data set, determine the nonlinear differential equation used to reconstruct the single-cell developmental trajectory based on the gene regulatory network, and then determine the probability distribution corresponding to the gene regulatory network based on the differential equation. Based on the probability distribution, each cell development state of the single cell can be arranged in chronological order on the corresponding trajectory, thereby generating an intuitive potential energy topography map for reflecting the developmental trajectory of the single cell, thereby realizing the reconstruction of the differentiation and developmental trajectory of single cells in the tissue. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 This is one of the flow charts of the method for reconstructing the developmental trajectory of a single cell provided by the present invention;

[0037] Figure 2 This is the second flow chart of the method for reconstructing the developmental trajectory of a single cell provided by the present invention;

[0038] Figure 3 Schematic diagram of the structure of the single-cell developmental trajectory reconstruction device provided by the present invention;

[0039] Figure 4 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0040] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0041] In order to facilitate a clearer understanding of the various embodiments of the present application, some relevant background knowledge is first introduced as follows.

[0042] With the rapid development of single-cell sequencing technology and the emergence of a large number of corresponding analysis tools, the application of single-cell sequencing has gradually matured, and the biological problems it can solve are becoming more and more extensive. Single-cell transcriptome sequencing can study the function and phenotype of cells at the individual cell level.

[0043] However, due to technical reasons, after a sample is subjected to single-cell transcriptome sequencing, the cell has already died, making it impossible to track subsequent changes in the cell. Cell trajectory analysis can reconstruct the changes in cells over time by constructing the trajectories of changes between cells, helping people infer the evolution and differentiation processes between cells at the single-cell level.

[0044] The emergence of numerous biological regulatory networks representing the relationships governing stem cell fate has enabled detailed analysis of cell differentiation and development. Currently, dynamic modeling of biomolecular networks and the use of kinetic analysis to unravel the regulatory mechanisms between molecules are key areas of research.

[0045] Cell trajectory analysis can reconstruct the temporal evolution of cells by constructing trajectories of change between cells, helping to infer the evolution and differentiation of cells at the single-cell level. This inference is primarily based on the similarity of expression profiles between cells and the ratio between the abundance of precursor (unspliced) and mature (spliced) mRNAs of the same transcript within a cell. However, such methods cannot determine the direction of cell differentiation, and the trajectory selection of cell differentiation and developmental pathways, particularly the underlying mechanisms of these changes, is unclear.

[0046] Therefore, the present invention starts from the perspective of the system, dynamically models the regulatory network based on nonlinear differential equations, combines the transcriptional state of the cell and the ratio between the precursor (unspliced) and mature (spliced) mRNA abundance, and performs generalized Perron cluster analysis on it. The initial, intermediate and terminal cell states in the biological system are first detected to obtain a global fate map and the probability of reaching each state. Through quantitative fitting of time series data, biologically known stable state expression data or expression data corresponding to different stable states obtained by the above analysis, dynamic model parameters are obtained. Performing kinetic analysis and stable state analysis on it can clearly understand the changes of each factor in the network at different times, explain the intrinsic mechanism of cell gene expression, and define and reveal the differentiation and development trajectory of cells. That is, according to the state of each cell, each cell can be arranged on the corresponding trajectory according to the pseudo-time, generating an intuitive cell lineage development dendrogram, thereby reconstructing the differentiation and development trajectory of cells in the tissue.

[0047] At the same time, by changing the external stimuli or other factors corresponding to the parameter changes of the model, the system's response to different stimuli and the changes in gene expression can be clearly analyzed and reconstructed.

[0048] The following combination Figures 1 to 2 The single-cell developmental trajectory reconstruction method provided by the present invention is described in detail. Figure 1 This is one of the flow charts of the method for reconstructing the developmental trajectory of a single cell provided by the present invention, see Figure 1 As shown, the method includes steps 101 to 104, wherein:

[0049] Step 101: Based on the gene dataset of a single cell, generate a gene regulatory network corresponding to the single cell.

[0050] First of all, it should be noted that the executor of the present invention can be any electronic device that can establish the developmental trajectory of a single cell, for example, it can be any one of a smart phone, a smart watch, a desktop computer, a laptop computer, etc.

[0051] In this embodiment, in order to reconstruct the developmental trajectory of a single cell, it is first necessary to obtain a gene dataset of the single cell, which includes the behavioral genes of the single cell.

[0052] By listing behavioral genes as a matrix of cells, we can then construct the gene regulatory network corresponding to a single cell.

[0053] In practical applications, the gene regulatory network (GRN), or regulatory network for short, is an abstract concept that refers to the network formed by the interaction between genes within a cell (or within a specific genome). Among the many interaction relationships, it specifically refers to the inter-gene interactions caused by gene regulation.

[0054] There are many types of gene regulatory networks, such as protein interaction networks, gene transcription regulatory networks, post-transcriptional regulatory networks, signal transduction networks, etc.

[0055] Step 102: Based on the gene regulatory network, determine a differential equation corresponding to the gene regulatory network, and use the differential equation to reconstruct the developmental trajectory of the single cell.

[0056] After generating the gene regulatory network corresponding to a single cell, it is necessary to construct a differential equation based on the gene regulatory network. The differential equation can be expressed by the following formula (1):

[0057]

[0058] Among them, x i represents the gene expression level of the i-th gene in the N gene nodes of the gene regulatory network; f i represents the regulatory power on the i-th gene; as well as is the regulation of other genes on the i-th gene; a ji with b ji represent the promotion / inhibition constant of the jth node on the ith node; k i x i represents the degradation of the i-th factor itself.

[0059] The first three terms in formula (1) do not take into account the influence of other factors, such as noise interference, external factors and possible gene leakage expression, so the fourth term L0c is added here. i x i To express the comprehensiveness of other factors. Among them, L0 represents the influence of other factors, and parameter c i is a binary variable. When external factors affect x in the network i When it works, c i =1, no effect, c i =0.

[0060] Without assuming that gene variables are independent of each other, related product terms can also be considered based on the regulatory network; in the case of transcription and translation delays of factors, the delay parameter τ can also be considered, which can be verified in the subsequent model solution.

[0061] Through the above methods, gene regulatory networks can be analyzed, and the trajectory of tissue differentiation and development within tissues can be analyzed and reconstructed from a dynamic perspective through nonlinear differential equations.

[0062] Step 103: Based on the differential equation, determine the probability distribution corresponding to the gene regulatory network; the probability distribution is used to assist in establishing the potential energy topography of the single cell.

[0063] In this embodiment, the state of a gene regulatory network can be represented by the corresponding probability distribution P(x1,...,x N ,t), while the diffusion equation gives the probability time evolution equation of some specific states. However, when the number of variables N in the system is large, the diffusion equation is difficult to solve.

[0064] Therefore, we first need to use the self-consistent field approximation to perform product decomposition on the probability distribution to reduce the dimension of the system. The probability distribution after product decomposition can be specifically expressed by the following formula (2):

[0065]

[0066] Then, the moment equation is approximated as a differential equation, i.e. To infer the probability distribution of the gene regulatory network, the multivariate Gaussian distribution is selected as the selection probability of the steady-state probability distribution of the gene regulatory network, which is specifically expressed by the following formulas (3) and (4):

[0067]

[0068]

[0069] in, is the mean, σ(t) is the covariance matrix, and the elements of matrix A are specified as D is the diffusion matrix.

[0070] Step 104: establishing the potential energy topography map based on the probability distribution, wherein the minimum transition path in the potential energy topography map is used to reflect the developmental trajectory of the single cell.

[0071] In this embodiment, a potential energy topography map reflecting the developmental trajectory of a single cell is created using the Minimum Action Paths (MAPs) algorithm based on the probability distribution. The potential energy topography map includes a minimum action path reflecting the developmental trajectory of a single cell, which is obtained using the MAPs algorithm.

[0072] Specifically, the MAPs algorithm is explained as follows:

[0073] minimize In principle, there are many paths starting from i and ending at j, but with different actions. From the definition of transition path S T [Φ ij ], it actually needs to minimize the speed Φ along the path ij and drive F(Φ ij ), since the movement always follows the driving direction, its action will be minimal. Therefore, the minimized transition path is used for analysis to quantify the transfer paths between different cell states of single cells, understand the transformation process of key states of single cells, explain the intrinsic mechanism of cell gene expression, and define and reveal the differentiation and developmental trajectory of cells.

[0074] In another implementation of this embodiment, the gene regulatory network can also be subjected to bifurcation analysis in dynamics theory. By changing the parameters of the system, the topological structure of the phase space will change. The parameter point at this time is the bifurcation point, which can clearly show the changes of each factor in the gene regulatory network at different times. By changing the external stimulus or other factors corresponding to the parameter changes of the gene regulatory network, the response of the gene regulatory network to different stimuli and the changes in gene expression can be clearly analyzed and reconstructed.

[0075] The single-cell developmental trajectory reconstruction method provided by the present invention generates a gene regulatory network corresponding to the single cell based on the single-cell dataset, determines a nonlinear differential equation for reconstructing the single-cell developmental trajectory based on the gene regulatory network, and then determines the probability distribution corresponding to the gene regulatory network based on the differential equation. Based on the probability distribution, each cell development state of the single cell can be arranged in chronological order on the corresponding trajectory, thereby generating an intuitive potential energy topography map for reflecting the developmental trajectory of the single cell, thereby realizing the reconstruction of the differentiation and developmental trajectory of single cells in the tissue.

[0076] Optionally, in a possible implementation of this embodiment, the gene regulatory network corresponding to the single cell is generated based on the single cell gene dataset, which can be specifically implemented by the following steps (1) to (2):

[0077] Step (1), when the gene regulatory network is a time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset;

[0078] Step (2): Optimizing the adjustable parameters of the initial gene regulatory network using a least squares algorithm to generate a gene regulatory network corresponding to the single cell.

[0079] In this embodiment, it is first necessary to generate an initial gene regulatory network corresponding to a single cell based on a gene dataset. The initial gene regulatory network includes basic parameters constituting the gene regulatory network, such as gene nodes.

[0080] For gene regulatory networks with known time series data, a nonlinear least squares algorithm is needed to obtain the minimum value of the sum of squared errors (yx) by using the time series y predicted by the model and the actual time series x obtained. 2 , the adjustable parameters in the initial gene regulatory network are estimated by the above method to seek the optimal solution of the adjustable parameters. Based on the optimal solution of the adjustable parameters, the gene regulatory network corresponding to the single cell can be obtained.

[0081] Optionally, in another possible implementation of this embodiment, the gene regulatory network corresponding to the single cell is generated based on the single cell gene dataset, which can be specifically implemented by the following steps [1] to [2]:

[0082] Step [1], when the gene regulatory network is not a time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset;

[0083] Step [2], based on the steady-state data of gene expression corresponding to the single cell, using a target algorithm to optimize the adjustable parameters of the initial gene regulatory network to generate the gene regulatory network corresponding to the single cell; the target algorithm includes at least one of the following: a random parameter search algorithm, a particle swarm algorithm, and a gradient descent algorithm.

[0084] In this embodiment, when the gene regulatory network is not based on time series, that is, for a gene regulatory network for which time series data cannot be obtained but for which steady-state data can be obtained biologically and steady-state expression data are available, it is first necessary to generate an initial gene regulatory network corresponding to a single cell based on the gene dataset. The initial gene regulatory network includes the basic parameters constituting the gene regulatory network, such as gene nodes.

[0085] In order to infer the adjustable parameters of the initial gene regulatory network, under the premise of steady-state data, random parameter search or particle swarm optimization is combined with gradient descent algorithm to minimize the gene expression value y of the i-th gene in the cell state α in the model and the gene expression value x of the i-th gene in the cell state α in the experiment, and then obtain the minimum value of the sum of squared errors (yx) 2 , thereby seeking the optimal solution of the adjustable parameters, and based on the optimal solution of the adjustable parameters, the gene regulatory network corresponding to the single cell can be obtained.

[0086] Optionally, the steady-state data is determined by following steps 1) to 2):

[0087] Step 1), performing Perron clustering on the ratio between the abundance of precursor messenger RNA mRNA and mature mRNA of the single cell and the cytoplasmic small RNA count matrix to determine a global fate map of the single cell, wherein the global fate map includes at least one cell state of the single cell, and the cell state includes an initial cell state, an intermediate cell state, and a terminal cell state;

[0088] Step 2) Determine the steady-state data based on the global fate map and the probability of the single cell reaching each cell state.

[0089] In this embodiment, when the gene regulatory network is not based on a time series, that is, for a gene regulatory network for which time series data cannot be obtained but the steady state is biologically known and steady-state expression data are available, it is necessary to perform generalized Perron cluster analysis on the transcriptional state of a single cell and the ratio between the abundance of pre-mRNA (unspliced) and mature mRNA (spliced) (also known as RNA velocity), as well as the cytoplasmic small RNA (scRNA) count matrix, to obtain a global fate map of the cell; wherein the scRNA count matrix is ​​generated from the original sequencing data.

[0090] Steady-state data is then determined based on the initial, intermediate, and terminal cell states of individual cells in the global fate map, as well as the probability of a single cell reaching each state. Specifically, the initial, intermediate, and terminal cell states of the system are detected to obtain a global fate map. Based on the different cell states in the global fate map and the corresponding probability of reaching each state, the expression data for the corresponding cell states are traced back and the averaged expression data is taken to obtain steady-state data.

[0091] Optionally, the determining of the potential energy topography of the single cell based on the probability distribution using a minimum transition path algorithm can be specifically achieved by following the steps [a] to [b]:

[0092] Step [a]: determining a potential function based on the probability distribution, wherein the potential function is used to construct a potential energy topography map of the single cell;

[0093] Step [b]: Based on the potential function, a minimum transition path algorithm is used to determine the potential energy topography of the single cell.

[0094] In this embodiment, the potential function can be calculated by the following formula (5):

[0095] U(x)=-ln(P ss (x)) (5)

[0096] Among them, U(x) represents the potential function, P ss (x) represents the steady-state probability distribution corresponding to the gene regulatory network.

[0097] After determining the potential function, it is used to construct the potential energy landform.

[0098] In the above embodiment, the potential energy topography map constructed based on the MAPs algorithm can reflect the development trajectory of single cells and clearly reflect the curve direction of single cell differentiation based on potential energy.

[0099] Optionally, after determining the potential energy topography of the single cell, since it is difficult to visualize the potential energy topography for gene regulatory networks with more than 3 elements, it is necessary to combine the Lyapunov stability method to theoretically analyze and judge the stability of all equilibrium states of the gene regulatory network in a more direct analytical manner. After all stable states are determined, the potential energy topography is once again drawn. This is achieved by the following steps [1]-[2]:

[0100] Step [1], determining all equilibrium points of the potential energy landform map based on the steady-state data;

[0101] Step [2]: According to Lyapunov's stability theory, all steady states in each equilibrium point are determined, and the potential energy topography map is updated.

[0102] In this embodiment, for situations where the gene regulatory network has more than three elements and the potential energy landscape is difficult to visualize, the stability of all equilibrium states of the system is first theoretically analyzed and judged in a more direct analytical manner by combining the Lyapunov stability method.

[0103] Specifically, solve the equilibrium point of the above differential equation model Search for a numerical solution x e , calculate the steady state of the gene regulatory network, and then calculate all the equilibrium points in the potential energy landscape. Since the potential energy landscape has a strong nonlinear property, all the numerical solutions in the potential energy landscape are searched out first.

[0104] For dynamic systems, not all equilibrium states are stable, and there may be saddle points and other situations. Therefore, we first use the second-order Taylor expansion to approximate the original equation, and use its second-order Taylor expansion It is x=x e The Jacobian matrix at this time is R(x), where R(x) is a high-order term. Then, according to Lyapunov's stability theory, the real part of the eigenvalue of the Jacobian matrix is ​​compared with 0. If the real part of the eigenvalue is less than 0, the corresponding equilibrium point is asymptotically stable; if it is less than 0, the corresponding equilibrium point is unstable. All steady states are determined from this, and this is used as a guide to draw the potential energy topography. The eigenvalue is calculated based on the Jacobian matrix.

[0105] Figure 2 This is the second flow chart of the method for reconstructing the developmental trajectory of a single cell provided by the present invention, see Figure 2 As shown, the method includes steps 201 to 211, wherein:

[0106] Step 201: Generate an initial gene regulatory network corresponding to a single cell based on a gene dataset.

[0107] Step 202: When the gene regulatory network is a time series-based gene regulatory network, the adjustable parameters of the initial gene regulatory network are optimized using a least squares algorithm to generate a gene regulatory network corresponding to a single cell.

[0108] Step 203: If the gene regulatory network is not a time series-based gene regulatory network, perform Perron clustering on the ratio between the abundance of precursor mRNA and mature mRNA of the single cell and the scRNA count matrix to determine a global fate map of the single cell, where the global fate map includes at least one cell state of the single cell, and the cell state includes an initial cell state, an intermediate cell state, and a terminal cell state.

[0109] Step 204: Determine steady-state data based on the global fate map and the probability of a single cell reaching each cell state.

[0110] Step 205: Based on the steady-state data of gene expression corresponding to the single cell, optimize the adjustable parameters of the initial gene regulatory network using a target algorithm to generate the gene regulatory network corresponding to the single cell; wherein the target algorithm includes at least one of the following: a random parameter search algorithm, a particle swarm algorithm, and a gradient descent algorithm.

[0111] It should be noted that the execution order of step 202 and steps 203 to 205 is not particular.

[0112] Step 206: Based on the gene regulatory network, determine a differential equation corresponding to the gene regulatory network, wherein the differential equation is used to reconstruct the developmental trajectory of a single cell.

[0113] Step 207: Determine the probability distribution corresponding to the gene regulatory network based on the differential equation, wherein the probability distribution is used to assist in establishing a potential energy topography map of a single cell.

[0114] Step 208: Determine a potential function based on the probability distribution, wherein the potential function is used to construct a potential energy topography map of the single cell.

[0115] Step 209: Based on the potential function, use the MAPs algorithm to determine the potential energy topography of the single cell.

[0116] Step 210: Determine all equilibrium points of the potential energy topography map based on the steady-state data.

[0117] Step 211: According to Lyapunov's stability theory, all steady states in each equilibrium point are determined, and the potential energy landscape map is updated.

[0118] The single-cell developmental trajectory reconstruction method provided by the present invention generates a gene regulatory network corresponding to the single cell based on the single-cell data set, determines a nonlinear differential equation for reconstructing the single-cell developmental trajectory based on the gene regulatory network, and then determines the probability distribution corresponding to the gene regulatory network based on the differential equation. Based on the probability distribution, the minimum transition path algorithm is used to arrange the developmental state of each cell of the single cell in chronological order on the corresponding trajectory, thereby generating an intuitive potential energy topography map for reflecting the developmental trajectory of the single cell, thereby realizing the reconstruction of the differentiation and developmental trajectory of the single cell in the tissue.

[0119] The following describes the single-cell developmental trajectory reconstruction device provided by the present invention. The single-cell developmental trajectory reconstruction device described below and the single-cell developmental trajectory reconstruction method described above can be referenced to each other. Figure 3 Schematic diagram of the structure of the single cell developmental trajectory reconstruction device provided by the present invention, such as Figure 3 As shown, the single cell developmental trajectory reconstruction device 300 includes: a generation module 301, a first determination module 302, a second determination module 303 and an establishment module 304, wherein:

[0120] A generation module 301 is configured to generate a gene regulatory network corresponding to a single cell based on a gene dataset of the single cell;

[0121] A first determining module 302 is configured to determine a differential equation corresponding to the gene regulatory network based on the gene regulatory network, wherein the differential equation is used to reconstruct the developmental trajectory of the single cell;

[0122] A second determination module 303 is configured to determine a probability distribution corresponding to the gene regulatory network based on the differential equation; the probability distribution is used to assist in establishing a potential energy topography map of the single cell;

[0123] The establishing module 304 is configured to establish the potential energy topography map based on the probability distribution, wherein the minimum transition path in the potential energy topography map is used to reflect the developmental trajectory of the single cell.

[0124] The single-cell developmental trajectory reconstruction device provided by the present invention generates a gene regulatory network corresponding to the single cell based on the single-cell data set, determines a nonlinear differential equation for reconstructing the single-cell developmental trajectory based on the gene regulatory network, and then determines the probability distribution corresponding to the gene regulatory network based on the differential equation. Based on the probability distribution, each cell development state of the single cell can be arranged in chronological order on the corresponding trajectory, thereby generating an intuitive potential energy topography map for reflecting the developmental trajectory of the single cell, thereby realizing the reconstruction of the differentiation and developmental trajectory of the single cell in the tissue.

[0125] Optionally, the generating module 301 is further configured to:

[0126] In a case where the gene regulatory network is a time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset;

[0127] The adjustable parameters of the initial gene regulatory network are optimized using a least squares algorithm to generate a gene regulatory network corresponding to the single cell.

[0128] Optionally, the generating module 301 is further configured to:

[0129] In a case where the gene regulatory network is a non-time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset;

[0130] Based on the steady-state data of gene expression corresponding to the single cell, the adjustable parameters of the initial gene regulatory network are optimized using a target algorithm to generate the gene regulatory network corresponding to the single cell; the target algorithm includes at least one of the following: a random parameter search algorithm, a particle swarm algorithm, and a gradient descent algorithm.

[0131] Optionally, the steady-state data is determined by:

[0132] performing Perron clustering on the ratio between the abundance of precursor messenger RNA (mRNA) and mature mRNA of the single cell and the cytoplasmic small RNA count matrix to determine a global fate map of the single cell, wherein the global fate map includes at least one cell state of the single cell, and the cell state includes an initial cell state, an intermediate cell state, and a terminal cell state;

[0133] The steady-state data is determined based on the global fate map and the probability of the single cell reaching each cell state.

[0134] Optionally, the establishing module 304 is further configured to:

[0135] Based on the probability distribution, determining a potential function, wherein the potential function is used to construct a potential energy topography map of the single cell;

[0136] Based on the potential function, a minimum transition path algorithm is used to determine the potential energy topography of the single cell.

[0137] Optionally, the device further comprises:

[0138] a third determining module, configured to determine all equilibrium points of the potential energy landform map based on the steady-state data;

[0139] An updating module is used to determine all steady states in each equilibrium point according to Lyapunov stability theory and to update the potential energy topography map.

[0140] Figure 4 Schematic diagram of the structure of the electronic device provided by the present invention, such as Figure 4 As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other via the communication bus 440. The processor 410 may call the logic instructions in the memory 430 to execute a method for reconstructing the developmental trajectory of a single cell, the method comprising: generating a gene regulatory network corresponding to the single cell based on a gene dataset of the single cell; determining a differential equation corresponding to the gene regulatory network based on the gene regulatory network, the differential equation being used to reconstruct the developmental trajectory of the single cell; determining a probability distribution corresponding to the gene regulatory network based on the differential equation; the probability distribution being used to assist in establishing a potential energy map of the single cell; and establishing the potential energy map based on the probability distribution, wherein the minimum transition path in the potential energy map is used to reflect the developmental trajectory of the single cell.

[0141] In addition, the logic instructions in the above-mentioned memory 430 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0142] On the other hand, the present invention also provides a computer program product, which includes a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the single-cell developmental trajectory reconstruction method provided by the above-mentioned methods, the method including: generating a gene regulatory network corresponding to the single cell based on the gene data set of the single cell; determining the differential equation corresponding to the gene regulatory network based on the gene regulatory network, and the differential equation is used to reconstruct the developmental trajectory of the single cell; determining the probability distribution corresponding to the gene regulatory network based on the differential equation; the probability distribution is used to assist in establishing a potential energy map of the single cell; establishing the potential energy map based on the probability distribution, wherein the minimum transition path in the potential energy map is used to reflect the developmental trajectory of the single cell.

[0143] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the single-cell developmental trajectory reconstruction method provided by the above-mentioned methods, the method comprising: generating a gene regulatory network corresponding to the single cell based on a gene data set of the single cell; determining a differential equation corresponding to the gene regulatory network based on the gene regulatory network, the differential equation being used to reconstruct the developmental trajectory of the single cell; determining a probability distribution corresponding to the gene regulatory network based on the differential equation; the probability distribution being used to assist in establishing a potential energy map of the single cell; establishing the potential energy map based on the probability distribution, wherein the minimum transition path in the potential energy map is used to reflect the developmental trajectory of the single cell.

[0144] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0145] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for reconstructing the developmental trajectory of a single cell, characterized in that: include: Based on the gene dataset of a single cell, generating a gene regulatory network corresponding to the single cell; Based on the gene regulatory network, determining a differential equation corresponding to the gene regulatory network, wherein the differential equation is used to reconstruct the developmental trajectory of the single cell; The differential equation can be expressed by the following formula (1): Among them, x i represents the gene expression level of the i-th gene in the N gene nodes of the gene regulatory network; f i represents the regulatory power on the i-th gene; as well as is the regulation of other genes on the i-th gene; a ji with b ji represent the promotion / inhibition constant of the jth node on the ith node; k i x i represents the degradation of the i-th factor itself; L0 represents the influence of other factors, and parameter c i is a binary variable. When external factors affect x in the network i When it works, c i =1, no effect, c i =0; Based on the differential equation, determining a probability distribution corresponding to the gene regulatory network; the probability distribution is used to assist in establishing a potential energy topography map of the single cell; Based on the probability distribution, the potential energy topography of the single cell is determined, wherein the minimum transition path in the potential energy topography is used to reflect the developmental trajectory of the single cell.

2. The method for reconstructing the developmental trajectory of a single cell according to claim 1, characterized in that: The method of generating a gene regulatory network corresponding to a single cell based on a single cell gene dataset includes: In a case where the gene regulatory network is a time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset; The adjustable parameters of the initial gene regulatory network are optimized using a least squares algorithm to generate a gene regulatory network corresponding to the single cell.

3. The method for reconstructing the developmental trajectory of a single cell according to claim 1, wherein: The method of generating a gene regulatory network corresponding to a single cell based on a single cell gene dataset includes: In a case where the gene regulatory network is a non-time series-based gene regulatory network, generating an initial gene regulatory network corresponding to the single cell based on the gene dataset; Based on the steady-state data of gene expression corresponding to the single cell, the adjustable parameters of the initial gene regulatory network are optimized using a target algorithm to generate the gene regulatory network corresponding to the single cell; the target algorithm includes at least one of the following: a random parameter search algorithm, a particle swarm algorithm, and a gradient descent algorithm.

4. The method for reconstructing the developmental trajectory of a single cell according to claim 3, wherein: The steady-state data are determined in the following manner: performing Perron clustering on the ratio between the abundance of precursor messenger RNA (mRNA) and mature mRNA of the single cell and the cytoplasmic small RNA count matrix to determine a global fate map of the single cell, wherein the global fate map includes at least one cell state of the single cell, and the cell state includes an initial cell state, an intermediate cell state, and a terminal cell state; The steady-state data is determined based on the global fate map and the probability of the single cell reaching each cell state.

5. The method for reconstructing the developmental trajectory of a single cell according to any one of claims 1 to 4, characterized in that: Determining the potential energy topography of the single cell based on the probability distribution includes: Based on the probability distribution, determining a potential function, wherein the potential function is used to construct a potential energy topography map of the single cell; Based on the potential function, a minimum transition path algorithm is used to determine the potential energy topography of the single cell.

6. The method for reconstructing the developmental trajectory of a single cell according to claim 3 or 4, characterized in that: After determining the potential energy topography of the single cell, the method further includes: determining all equilibrium points of the potential energy topography map based on the steady-state data; According to Lyapunov's stability theory, all steady states in each equilibrium point are determined, and the potential energy topography map is updated.

7. A single-cell developmental trajectory reconstruction device, characterized in that: include: A generation module, configured to generate a gene regulatory network corresponding to a single cell based on a gene dataset of the single cell; A first determination module is configured to determine a differential equation corresponding to the gene regulatory network based on the gene regulatory network, wherein the differential equation is used to reconstruct the developmental trajectory of the single cell; A second determination module is configured to determine a probability distribution corresponding to the gene regulatory network based on the differential equation; the probability distribution is used to assist in establishing a potential energy topography map of the single cell; The differential equation can be expressed by the following formula (1): Among them, x i represents the gene expression level of the i-th gene in the N gene nodes of the gene regulatory network; f i represents the regulatory power on the i-th gene; as well as is the regulation of other genes on the i-th gene; a ji with b ji represent the promotion / inhibition constant of the jth node on the ith node; k i x i represents the degradation of the i-th factor itself; L0 represents the influence of other factors, and parameter c i is a binary variable. When external factors affect x in the network i When it works, c i =1, no effect, c i =0; A module is established for determining the potential energy topography of the single cell based on the probability distribution, wherein the minimum transition path in the potential energy topography is used to reflect the developmental trajectory of the single cell.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the single-cell developmental trajectory reconstruction method according to any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for reconstructing the developmental trajectory of a single cell as claimed in any one of claims 1 to 6 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for reconstructing the developmental trajectory of a single cell as claimed in any one of claims 1 to 6 is implemented.

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