Intervention device, intervention method, and program

Abstract

To provide an intervention device capable of estimating which factors governing the state of the system should be intervened in order to return the system to then original stable state just before the system transitions from the stable state to a critical state.SOLUTION: An intervention device 1 for suppressing fluctuations in networks where nodes with state quantities are connected includes: a state sample acquiring unit 11 that acquires multiple samples of state; an estimation unit 12; an intervention unit 13; and a control unit 14. The estimation unit 12 selects eigenvectors related to the eigenvalues of the covariance matrix of the acquired multiple samples as an estimate of the dominant right eigenvector. The control unit 14 is configured to control the intervention unit 13 so as to intervene to suppress the state quantity corresponding to the eigenvector component related to the selected eigenvalue on the network.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to an intervention device, an intervention method, and a program. [Background technology]

[0002] In natural phenomena (e.g., the onset of disease, earthquakes, climate change, etc.) and social phenomena (e.g., road traffic volume, electricity consumption, fluctuations in foreign exchange and stock prices, etc.), when a system reaches a "critical state" (hereinafter also referred to as a "branch point" or "tipping point"), a sudden transition from a previous stable state to another stable state can occur (see, for example, Non-Patent Documents 1 to 5). For example, in the case of a living organism, a person who has been stably healthy up to a certain point reaches a "pre-critical state" (the state immediately before the critical state), which is a "pre-disease state" (a state in which the person is moving away from a healthy state, but has not yet developed a disease), and then the state suddenly transitions to a disease, and the disease state continues. If we can detect such pre-critical states (i.e., signs of a sudden state transition), it is thought that we can respond to sudden changes and phenomena in natural and social phenomena, including disease.

[0003] The following description focuses on biological systems (especially biological networks in which a living organism is modeled as a network) as the target system. However, it should be understood that the technology disclosed herein is not limited to biological systems, but can be widely applied to natural and social systems whose state changes due to some factor, such as crustal systems, meteorological systems, ecosystems, transportation systems, power systems, and financial systems.

[0004] Regarding research into the dynamic mechanisms of disease, it is known that the progression process of disease worsening (e.g., asthma attacks, onset of cancer) is modeled as a time-dependent nonlinear dynamic system, and by analyzing this, a relationship between state transitions at branching points and sudden worsening of the disease has been discovered (see, for example, non-patent document 6).

[0005] Against this background, a technology for detecting candidates for dynamic network markers (DNMs), which serve as indicators of the state of a system, has been disclosed (see, for example, Patent Document 1). In the case of a living organism, a DNM is also called a dynamic network biomarker (DNB), based on measurement data of multiple factor items obtained by measuring the organism. Furthermore, a technology has been disclosed for detecting a pre-disease state between a healthy state and a diseased state, in which changes in the state of a target factor and the connecting factors that are dynamically and directly connected to this factor are regarded as local network entropy, and the pre-disease state is detected based on this local network entropy (see, for example, Patent Document 2). Furthermore, a technology has been disclosed for determining whether a DNB has occurred by storing data obtained by collecting and analyzing biological materials from multiple healthy individuals and adding analytical data from a biological material collected only once from a subject (see, for example, Patent Document 3). [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent Publication No. 2014-64515 [Patent Document 2] Patent Publication No. 2014-83194 [Patent Document 3] International Publication No. 2018 / 207925 [Non-patent literature]

[0007] [Non-Patent Document 1] [ PubMed ] Jose G. Venegas, Tilo Winkler, Guido Musch, Marcos F. Vidal Melo, Dominick Layfield, Nora Tgavalekos, Alan J. Fischman, Ronald J. Callahan, Giacomo Bellani, and R. Scott Harris. 777-782 (2005)

Outdoor Tool2

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Direct Environment 5

[0008] The techniques disclosed in Patent Documents 1 to 3 can detect signs of a transition from a healthy state to a diseased state. If a pre-disease state is detected in this way, and appropriate early treatment can be administered at this stage (i.e., before the diseased state is reached) to restore the patient to a healthy state, this is expected to have the excellent effect of reducing treatment costs and increasing the chances of recovery. To achieve such early treatment, it is necessary to know what kind of intervention should be applied to which part of the biological network corresponding to the pre-disease state. In other words, when a system (biological network) transitions from a stable state (healthy state) to a pre-critical state (pre-disease state), it is necessary to estimate which factor (e.g., mRNA) governing the state of the system (biological network) should be intervened in order to restore the system (biological network) to its original stable state (healthy state). However, basic research into methods for estimating such interventions has only just begun, and many issues remain unresolved.

[0009] The present invention has been made in view of these circumstances, and its purpose is to estimate which factor, among the factors that govern the state of a system, should be intervened in order to return the system to its original stable state immediately before the system is about to transition from a stable state to a critical state. [Means for solving the problem]

[0010] In order to solve the above problem, one aspect of the present invention provides an intervention device for suppressing fluctuations in a network in which nodes having state quantities are connected to one another, and includes a state quantity sample acquisition unit that acquires multiple samples of the state quantities, an estimation unit, an intervention unit, and a control unit. The estimation unit selects an eigenvector related to an eigenvalue of a covariance matrix of the multiple acquired samples as an estimate of a dominant right eigenvector, and the control unit controls the intervention unit to intervene in the network in a direction that suppresses the state quantity corresponding to a component of the eigenvector related to the selected eigenvalue.

[0011] The term "dominant right eigenvector" will be explained in the detailed description section.

[0012] In one embodiment, the control unit may control the intervention unit so that, when fluctuations in the network are not suppressed, the intervention unit intervenes in the network in a direction that promotes a state quantity corresponding to a component of the selected eigenvector.

[0013] In one embodiment, the estimation unit may select the eigenvector associated with the largest eigenvalue among the eigenvalues ​​of the covariance matrix of the acquired samples as the estimate of the dominant right eigenvector.

[0014] In one embodiment, the control unit may control the intervention unit to intervene in the network with respect to a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector related to the largest selected eigenvalue.

[0015] In one embodiment, the control unit may control the intervention unit so that, when network fluctuations are not suppressed, the intervention unit intervenes in the network in a direction to suppress state quantities corresponding to components different from the components of the selected eigenvector.

[0016] In one embodiment, the network may be a biological network in which genes are connected to one another.

[0017] In one embodiment, the state quantity may be the expression level of mRNA of a gene.

[0018] Another aspect of the present invention is a method for suppressing fluctuations in a network in which nodes having state quantities are connected to one another, the method including a state quantity sample acquisition step of acquiring a plurality of samples of the state quantities, an estimation step, and an intervention step. The estimation step selects an eigenvector related to the eigenvalues ​​of a covariance matrix of the acquired plurality of samples as an estimate of a dominant right eigenvector, and the intervention step performs intervention on the network in a direction to suppress the state quantity corresponding to a component of the selected eigenvector.

[0019] In one embodiment, when the fluctuations of the network are not suppressed, the intervention step may involve performing an intervention on the network in a direction that promotes a state quantity corresponding to a component of the selected eigenvector.

[0020] In one embodiment, the estimation step may select the eigenvector associated with the largest eigenvalue among the eigenvalues ​​of the covariance matrix of the acquired samples as the estimate of the dominant right eigenvector.

[0021] In one embodiment, the intervention step may involve performing intervention on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector associated with the largest selected eigenvalue.

[0022] In one embodiment, when the fluctuations of the network are not suppressed, the intervention step may involve intervening in the network in a direction to suppress a state quantity corresponding to a component other than the component of the eigenvector associated with the largest selected eigenvalue.

[0023] Another aspect of the present invention is a computer program. The program causes a computer to execute a method including a state quantity sample acquisition step of acquiring a plurality of state quantity samples, an estimation step, and an intervention step. The estimation step selects an eigenvector related to the eigenvalues ​​of the covariance matrix of the acquired plurality of samples as an estimate of the dominant right eigenvector. The intervention step performs intervention on the network in a direction that suppresses the state quantity corresponding to the component of the selected eigenvector.

[0024] In one embodiment, the program may cause a computer to execute a method in which, when fluctuations in the network are not suppressed, the intervention step involves intervening in the network in a direction that promotes a state quantity corresponding to a component of the selected eigenvector.

[0025] In one embodiment, the program may cause a computer to execute a method in which, when fluctuations in the network are not suppressed, the intervention step intervenes in the network in a direction to suppress state quantities corresponding to components different from the components of the selected eigenvector.

[0026] Any combination of the above components, and any transformation of the present invention into an apparatus, method, system, recording medium, computer program, etc., are also valid aspects of the present invention. [Effects of the Invention]

[0027] According to the present invention, it is possible to estimate which of the factors governing the state of a system should be intervened in order to return the system to its original stable state immediately before the system is about to transition from a stable state to a critical state. [Brief explanation of the drawings]

[0028] [Figure 1] FIG. 1 is a diagram illustrating the distribution of eigenvalues ​​of a matrix A on a complex plane. [Figure 2] FIG. 1 is a schematic diagram illustrating the concept of the technology according to the present disclosure. [Figure 3] FIG. 1 is a schematic diagram illustrating the concept of the technology according to the present disclosure. [Figure 4] FIG. 1 is a functional block diagram of an intervention device according to a first embodiment. [Figure 5] FIG. 4 is a functional block diagram of an intervention device according to second, third and fourth embodiments. [Figure 6] 13 is a flowchart showing a processing procedure of an intervention method according to a fifth embodiment. [Figure 7] 13 is a flowchart showing a processing procedure of an intervention method according to a sixth embodiment. [Figure 8] 13 is a flowchart showing a processing procedure of an intervention method according to a seventh embodiment. [Figure 9] FIG. 1 is a diagram showing a network structure used in a simulation. [Figure 10] FIG. 2 is a diagram illustrating the state of each node in the network. [Figure 11] 11(a) and 11(b) show the values ​​of the components of the dominant right and left eigenvectors, respectively. [Figure 12] FIG. 10 illustrates the product of a dominant right eigenvector and a dominant left eigenvector. [Figure 13] 1 is a graph showing the results of a real-time PCR analysis of the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. [Figure 14] 1 is a graph showing the results of a real-time PCR analysis of the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. [Figure 15] 1 is a graph showing the results of a real-time PCR analysis of the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. [Figure 16] 1 is a graph showing the results of a real-time PCR analysis of the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. [Figure 17] 1 is a graph showing the results of a real-time PCR analysis of the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. [Figure 18] 1 is a graph showing the results of a real-time PCR analysis of the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. DETAILED DESCRIPTION OF THE INVENTION

[0029] The present invention will be described below based on preferred embodiments with reference to the drawings. In the embodiments and modifications, identical or equivalent components and members are designated by the same reference numerals, and redundant descriptions will be omitted where appropriate. The dimensions of the components in the drawings are enlarged or reduced as appropriate for ease of understanding. Some components that are not important for explaining the embodiments are omitted from the drawings. Terms including ordinal numbers such as "first" and "second" are used to describe various components, but these terms are used only to distinguish one component from another and do not limit the components.

[0030] Before describing specific embodiments, we will first describe the underlying findings. In the DNM theory described above, a healthy state and a diseased state are considered to be different energetically stable states. Based on this, we focus on the pre-disease state, which occurs when a healthy state changes suddenly to a diseased state. In the pre-disease state, the stability is weaker than in the healthy state, and fluctuations in biological data such as mRNA expression levels become greater. If this state is left unchecked, it will transition to a diseased state, which is another stable state. From an energetic perspective, it is clear that a great deal of effort is required to restore a diseased state to a healthy state.

[0031] Therefore, the idea is to treat the disease at the pre-disease stage, reducing fluctuations to a healthy state and restoring the original healthy state. DNM theory extracts multiple genes (hereafter referred to as "DNM genes" or "DNM nodes") with high correlations between their fluctuations and the expression levels of other genes from mRNA expression data and focuses on the gene network they form. DNM intervention involves identifying dominant genes among all genes, including these DNM genes, and intervening in their expression (i.e., suppressing or promoting) to reduce the fluctuations of the DNM genes. However, as will be discussed later, genes with high fluctuations are not necessarily the targets of intervention. From this perspective, the DNM intervention problem boils down to the problem of predicting "which genes" and "whether to suppress or promote the expression of the genes" based on mRNA and other expression data in the gene network.

[0032] From the perspective of control theory, the DNM intervention problem can be seen as the restabilization of biodynamics. In other words, a previously stable healthy state is considered to be a state in which the stability of biodynamics declines due to changes in external factors such as reaction constants in gene expression, resulting in a pre-disease state. DNM intervention aims to raise this once-decreased stability back up, i.e., to restabilize it. The key issue here is which gene (or genes) mRNA expression should be suppressed or promoted in order to control stability.

[0033] To solve this problem, we consider the phenomenon of mRNA expression in a gene network as a system in which each gene interacts with the other in mRNA expression. Based on this, we interpret the stability described above as equivalent to the stability of a dynamical system (differential equation) that determines the expression rate of each mRNA.

[0034] Let's explain the above intuitively using an analogy. Imagine a situation in which multiple balls are connected by springs (asymmetric springs, to be precise) to form a network. In this case, let's say that one ball is swaying the most, and consider which ball's fluctuations need to be suppressed to suppress the overall fluctuation. Even if you suppress the ball that is swaying the most, it does not necessarily mean that the fluctuations of the ball next to it will be weakened. This is because if the spring constant of the ball connected to it is low or if the mass of the ball next to it is large, the effect of suppressing the swing of that ball will hardly be transmitted to the neighboring ball. In this way, in the case of a network of balls connected by springs, it can be seen that which ball should be suppressed to suppress the overall fluctuation depends on the structure of the entire network.

[0035] The above analogy can also be applied to gene networks. However, it is important to note that in the case of high-dimensional and complex network structures such as gene networks, it is generally possible to grasp only a portion of the overall structure. Furthermore, it is often difficult to obtain a sufficient number of gene mRNA expression levels over time, and only a few samples at most can be obtained at each time point.

[0036] The following description focuses on biological systems as target systems. Biological systems are modeled as networks. In this case, the nodes that are connected to each other to form the network are genes. Each gene has an mRNA expression level as a state quantity. However, the networks targeted by this disclosure are not limited to this, and any type of network can be used, such as crustal systems, meteorological systems, ecosystems, transportation systems, power systems, and financial systems, as long as the network is composed of nodes with state quantities.

[0037] Unless otherwise specified, z(t) is an n-dimensional column vector representing the expression level of mRNA, where n is the number of nodes. e is an n-dimensional column vector that represents the stable point (equilibrium point) of mRNA expression level. x(t)=z(t)-z eis an n-dimensional column vector that represents the deviation (fluctuation) of mRNA expression level from the stable point (equilibrium point). T Let (t) denote the transposed column vector of x(t). Also, x(t) is sometimes abbreviated as simply x.

[0038] Generally, a high-dimensional network system can be modeled as a nonlinear dynamical system, but in this specification, we assume that the time change of x(t) can be approximated by the following linear system.

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[0039] As an example, consider the case where A is:

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[0040] The above example assumes that it is known which interactions between state variables contribute most to the overall system fluctuation. However, as mentioned above, high-dimensional network structures such as gene networks can only be partially understood, and only a limited number of state variables can be sampled. Therefore, it is difficult to determine which interactions between state variables contribute most to the overall system fluctuation. In other words, it is difficult to identify the system matrix A. Therefore, it is impossible to obtain an exact solution by solving the stabilization problem used in conventional control theory. This has been a major factor that has traditionally made it difficult to restore a stable state from a pre-critical state through intervention. To address this unresolved issue, the inventors discovered that by following the steps below, it is possible to estimate the state variables that contribute most to the fluctuation, and therefore to stabilize the system by intervening in those state variables.

[0041] (Step 1) Samples of expression levels z(t) of multiple mRNAs in a pre-disease state are obtained.

[0042] The number of samples may be relatively small. For example, in this specification, several to several tens of samples are assumed, but the number of samples is not limited to this and may be any number. As mentioned above, z e When (t) is an n-dimensional column vector representing the stable point (equilibrium point) of mRNA expression level, x(t) = z(t) - z eLet (t) be an n-dimensional column vector that represents the deviation (fluctuation) of mRNA expression level from the stable point (equilibrium point).

[0043] (Step 2) covariance matrix E[x(t)x of z(t) T (t)] and E[x(t)x T (t)], the largest eigenvalue λ d Eigenvector v with respect to d is calculated and selected as an estimate of the dominant right eigenvector. Here, if the eigenvalue λ1(M) represents the eigenvalue of matrix M with the largest real part, the right eigenvector corresponding to the eigenvalue λ1(A) of the system matrix A is called the dominant right eigenvector and is denoted by v1. Also, its left eigenvector is called the dominant left eigenvector and is denoted by w1.

[0044] λ d is sometimes called the "dominant eigenvalue". Also, the above covariance matrix E[x(t)x T (t)] is a covariance matrix for a limited number of mRNA expression samples, so it is sometimes called the "sample covariance matrix." d is sometimes called the "dominant eigenvector of the sample covariance matrix." Note that since the sample covariance matrix is ​​a symmetric matrix, the right eigenvector and the left eigenvector are the same. In the pre-critical state (pre-disease state), this v d is known to be a good approximation of v1. In other words, the dominant eigenvector v of the sample covariance matrix is d is an estimate of the dominant right eigenvector v1 of the system matrix A.

[0045] In contrast, no effective method has been found to date for estimating the dominant left eigenvector w1.

[0046] (Step 3) The dominant eigenvector v of the sample covariance matrix obtained in step 2 d The component with the largest absolute value is v d (i max) and this i max Intervention is performed to suppress the expression of mRNA for the corresponding gene.

[0047] At this time

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[0048] In the following, we first provide a preliminary explanation assuming that matrix A is known. Figure 1 shows the distribution of eigenvalues ​​of matrix A on the complex plane. The points marked with × are eigenvalues. When matrix A (which is assumed to be diagonalizable in this specification) has a rank of n, there are n nonzero eigenvalues, including multiplicities. Among these eigenvalues, λ1, which is closest to the imaginary axis, is referred to here as the dominant eigenvalue (the eigenvalue corresponding to the dominant right eigenvector v1). This is because, when matrix A is eigenvalue decomposed, the state component associated with λ1 closest to the imaginary axis (i.e., closest to zero) converges the slowest and therefore contributes most to fluctuations. The closer λ1 is to the imaginary axis (i.e., the closer λ1 is to zero), the greater the fluctuations, and the closer the system approaches bifurcation. Therefore, as indicated by the arrows in Figure 1, it is believed that the system can be restored to a stable state by intervening in the system to move λ1 further away from the imaginary axis (i.e., by reducing λ1). In Figure 1, we intervene in the system to change λ1 to λ s This shows how the image has been changed to

[0049] The example in Figure 1 shows an eigenvalue crossing the imaginary axis of the complex plane at a single point (the origin), such as a saddle-node bifurcation (tangent bifurcation). Therefore, in this example, the dominant eigenvalue is a real number. However, this is not limited to this case; the above concept can also be applied to cases where two complex conjugate eigenvalues ​​cross the imaginary axis, such as a Hopf bifurcation. In this case, two eigenvectors are found from the sample covariance matrix. Furthermore, genes corresponding to components with large absolute values ​​of the real and imaginary parts of the complex eigenvectors corresponding to the complex eigenvalues ​​of matrix A are candidates for intervention. In other words, two gene candidates are available: one for a gene corresponding to a component with a large absolute value of the real part, and the other for a gene corresponding to a component with a large absolute value of the imaginary part. Furthermore, there are two types of candidates, inhibitory and stimulatory, for a total of four candidates.

[0050] From this preliminary explanation, we return to the explanation of (Step 3). As mentioned above, in a real gene network structure, matrix A is unknown, and it is not known which gene to actually intervene in, nor is it known in which direction (inhibition or promotion) to intervene in the expression of the mRNA of that gene.

[0051] In response to this, the inventors have conducted research and have found the following.

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[0052] The reason why components of the dominant right eigenvector with larger absolute values ​​are more advantageous for stabilizing the network can be intuitively explained as follows. The behavior of this system is determined by the overlap of multiple modes (which can be thought of as predetermined frequency signals) that determine the rate of change. The most dominant mode that determines fluctuations in mRNA expression levels in the pre-disease state is characterized by the dominant right eigenvector. Therefore, it is thought that genes that are advantageous for intervention are among the genes corresponding to components of this eigenvector with larger absolute values.

[0053] As explained above, by following the steps (Step 1) to (Step 3), the system can be returned to its original stable state with a relatively high degree of accuracy, thereby solving the problem of the present disclosure.

[0054] However, w1(i max ) has the opposite sign, intervention in the suppression direction in step 3 will cause λ1 to approach the imaginary axis (i.e., λ1 will become larger). In such a case, steps (step 1) to (step 3) alone will not only fail to suppress the fluctuations of the entire system, but may actually increase the fluctuations. In response to this, the inventors have discovered that by performing the following step (step 4) after step 3, fluctuations can be suppressed with a higher degree of accuracy.

[0055] (Step 4) If fluctuations cannot be suppressed in (Step 1) to (Step 3), max The target gene is a gene that is involved in the transcription of a gene, and the target gene is a gene that is involved in the transcription of a gene.

[0056] In this way, by intervening in the opposite direction to that of (Step 3) (i.e., in the direction of promoting mRNA expression) in (Step 4), fluctuations can be suppressed even in cases where overall fluctuations cannot be suppressed even after following steps (Step 1) to (Step 3).

[0057] However, w1(i max ) is extremely close to zero,

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[0058] (Step 5) The dominant right eigenvector v of the sample covariance matrix obtained in step 3 d The component with the second largest absolute value is v d (i max2 ) and this i max2 Intervention is performed to suppress the expression of mRNA for the corresponding gene.

[0059] In this way (step 5), i max instead of i max2 By intervening to suppress the expression of the mRNA of the gene corresponding to the above, it is possible to suppress the fluctuation even if steps (Step 1) to (Step 4) have not been successful in suppressing the overall fluctuation.

[0060] If the fluctuations in the entire system cannot be suppressed by steps (Step 1) to (Step 5) alone, the process returns to step (Step 4) and the same process can be repeated until the fluctuations can be suppressed.

[0061] 2 and 3 schematically show the concept of the technology according to the present disclosure described above.

[0062] [First embodiment] FIG. 4 shows a functional block diagram of an intervention device 1 according to a first embodiment. The intervention device 1 intervenes in a network in which nodes having state quantities are connected to each other, and suppresses fluctuations in the network. The intervention device 1 includes a state quantity sample acquisition unit 11, an estimation unit 12, and an intervention unit 13.

[0063] The state quantity sample acquisition unit 11 acquires a plurality of state quantity samples. The number of samples may be extremely small. For example, when the target network is a gene network, the samples may be mRNA expression levels acquired by a DNA sequencer.

[0064] The estimation unit 12 obtains a covariance matrix of the multiple samples acquired by the state quantity sample acquisition unit 11. Then, the estimation unit 12 calculates the eigenvector associated with the largest eigenvalue among the eigenvalues ​​of the covariance matrix, and selects this as an estimate of the dominant right eigenvector.

[0065] The intervention unit 13 intervenes in the target network to suppress fluctuations in the network. Specifically, the intervention unit 13 targets a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected by the estimation unit 12, and intervenes to suppress this state quantity.

[0066] According to this embodiment, when the target network transitions from a stable state to a pre-critical state (i.e., when fluctuations occur in the network), it is possible to estimate which state variables constituting the network should be intervened in to suppress the fluctuations in order to return the network to its original stable state.

[0067] [Second embodiment] 5 shows a functional block diagram of an intervention device 2 according to the second embodiment. The intervention device 2 includes a state quantity sample acquisition unit 11, an estimation unit 12, an intervention unit 13, and a control unit 14. That is, the intervention device 2 includes the control unit 14 in addition to the configuration of the intervention device 1 shown in FIG. 4. The other configurations and operations of the intervention device 2 are the same as those of the intervention device 1.

[0068] When the network fluctuation is not suppressed, the control unit 14 controls the intervention unit 13. Specifically, the control unit 14 controls the intervention unit 13 to intervene in the target network in a direction that promotes a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected by the estimation unit 12.

[0069] According to this embodiment, fluctuations in the target network can be suppressed with a higher degree of accuracy.

[0070] [Third embodiment] A third embodiment will be described with reference to Fig. 5. In the third embodiment, when fluctuations in the network are not suppressed, the control unit 14 controls the intervention unit 13 so that the intervention unit 13 intervenes in the target network in a direction to suppress a state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected by the estimation unit 12.

[0071] According to this embodiment, fluctuations in the target network can be suppressed with even higher accuracy.

[0072] [Fourth embodiment] A fourth embodiment will be described with reference to Fig. 5. In the fourth embodiment, when the fluctuation of the network is not suppressed even after intervention in a direction to suppress the state quantity corresponding to the component with the second largest absolute value, the control unit 14 controls the intervention unit 13 to intervene in the network in a direction to promote the state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected by the estimating unit 12. When the fluctuation of the network is still not suppressed, the control unit 14 controls the estimating unit 12 and the intervention unit 13 so that the intervention unit 13 intervenes in the network in a direction to suppress the state quantity corresponding to the component with the third largest absolute value among the components of the eigenvector selected by the estimating unit 12.

[0073] Similarly, if the network fluctuation is not suppressed even after intervention in the suppressing direction, the control unit 14 controls the intervention unit 13 to intervene in the promoting direction. If the network fluctuation is still not suppressed, the control unit 14 controls the estimation unit 12 and the intervention unit 13 to intervene in the suppressing direction to suppress the state quantity corresponding to the component with the next largest absolute value among the components of the eigenvector selected by the estimation unit 12. The control unit 14 repeats the above processing procedure, controlling the estimation unit 12 and the intervention unit 13, until the network fluctuation is suppressed.

[0074] According to this embodiment, fluctuations in the target network can be suppressed with even higher accuracy.

[0075] [Fifth embodiment] 6 is a flowchart showing the processing steps of an intervention method according to the fifth embodiment. This method includes step S1 of acquiring samples of state quantities, step S2 of estimating a dominant right eigenvector, and step S3 of implementing intervention in the suppression direction on the state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2.

[0076] In step S1, the method obtains a number of samples of the state quantities, the number of samples being optionally very small.

[0077] In step S2, the method calculates a covariance matrix of the samples acquired in step S1, and then calculates the eigenvector associated with the largest eigenvalue of the covariance matrix, and selects this as an estimate of the dominant right eigenvector.

[0078] In step S3, this method intervenes in the target network to suppress fluctuations in the network. Specifically, in step S3, the state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2 is targeted, and intervention is performed to suppress this.

[0079] According to this embodiment, when the target network transitions from a stable state to a pre-critical state (i.e., when fluctuations occur in the network), it is possible to estimate which state variables constituting the network should be intervened in to suppress the fluctuations in order to return the network to its original stable state.

[0080] [Sixth embodiment] 7 is a flowchart showing the processing steps of an intervention method according to a sixth embodiment. This method includes step S1 of acquiring samples of state quantities, step S2 of estimating a dominant right eigenvector, step S3 of implementing suppressive intervention on the state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, step S4 of determining whether fluctuations have been suppressed, and step S5 of implementing facilitative intervention on the state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2. That is, the intervention method according to the sixth embodiment includes step S4 and step S5 following step S3 of the intervention method according to the fifth embodiment.

[0081] In step S4, the method determines whether fluctuations in the target network have been suppressed by the processes from step S1 to step S3. If the determination result is affirmative, the process ends. If the determination result is negative, the process proceeds to step S5.

[0082] In step S5, the method targets the state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, and performs intervention in a direction to promote this.

[0083] According to this embodiment, fluctuations in the target network can be suppressed with a higher degree of accuracy.

[0084] [Seventh embodiment] 8 is a flowchart showing the processing steps of an intervention method according to a seventh embodiment. This method includes step S1 of acquiring samples of state quantities, step S2 of estimating a dominant right eigenvector, step S3 of implementing a suppression intervention on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, step S4 of determining whether fluctuations have been suppressed, step S5 of implementing a promotion intervention on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, step S6 of determining whether fluctuations have been suppressed, and step S7 of implementing a suppression intervention on a state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected in step S2. That is, the intervention method according to the seventh embodiment includes step S6 and step S7 following step S5 of the intervention method according to the sixth embodiment.

[0085] In step S6, the method determines whether fluctuations in the target network have been suppressed by the processes from step S1 to step S5. If the determination result is affirmative, the process ends. If the determination result is negative, the process proceeds to step S7.

[0086] In step S7, the method targets the state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected in step S2, and intervenes to suppress this.

[0087] According to this embodiment, fluctuations in the target network can be suppressed with even higher accuracy.

[0088] [Eighth embodiment] In the eighth embodiment, if the fluctuation of the network is not suppressed even after intervention in the direction of suppressing the state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected in step S2, intervention step S5 intervenes in the network in the direction of promoting the state quantity corresponding to the second largest component among the components of the eigenvector selected in estimation step S2. If the fluctuation of the network is still not suppressed, intervention step S5 intervenes in the network in the direction of suppressing the state quantity corresponding to the component with the third largest absolute value among the components of the eigenvector selected in estimation step S2.

[0089] Similarly, if the network fluctuation is not suppressed even after intervention in the suppression direction, intervention in the promotion direction is performed in the intervention step S5. If the network fluctuation is still not suppressed, intervention step S5 intervenes in the direction of suppressing the state quantity corresponding to the component with the next largest absolute value among the components of the eigenvector selected in step S2. Intervention step S5 repeats the above processing procedure until the network fluctuation is suppressed.

[0090] According to this embodiment, fluctuations in the target network can be suppressed with even higher accuracy.

[0091] [Ninth embodiment] The ninth embodiment is a computer program that causes a computer to execute a method including step S1 of acquiring samples of a state quantity, step S2 of estimating a dominant right eigenvector, and step S3 of implementing an intervention in a suppressive direction on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, as shown in Fig. 6 .

[0092] According to this embodiment, when the target network transitions from a stable state to a pre-critical state (i.e., when fluctuations occur in the network), in order to return the network to its original stable state, a method can be implemented as a software program to estimate which state variables constituting the network should be intervened in to suppress the fluctuations.

[0093] [Tenth embodiment] The tenth embodiment is also a computer program, which causes a computer to execute a method including the steps of: step S1 acquiring a sample of a state quantity; step S2 estimating a dominant right eigenvector; step S3 implementing an intervention in a suppressing direction on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2; step S4 determining whether the fluctuation has been suppressed; and step S5 implementing an intervention in a promoting direction on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, as shown in Fig. 7 .

[0094] According to this embodiment, a method that can suppress fluctuations in a target network with higher accuracy can be implemented as a software program.

[0095] [Eleventh embodiment] The eleventh embodiment is also a computer program, which causes a computer to execute a method including, as shown in Fig. 8, step S1 of acquiring a sample of a state quantity, step S2 of estimating a dominant right eigenvector, step S3 of implementing an intervention in a suppressing direction on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, step S4 of determining whether fluctuations have been suppressed, step S5 of implementing an intervention in a promoting direction on a state quantity corresponding to the component with the largest absolute value among the components of the eigenvector selected in step S2, step S6 of determining whether fluctuations have been suppressed, and step S7 of implementing an intervention in a suppressing direction on a state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected in step S2.

[0096] According to this embodiment, fluctuations in the target network can be suppressed with even higher accuracy.

[0097] [Twelfth embodiment] A twelfth embodiment is also a computer program. In this program, when the fluctuation of the network is not suppressed even after intervention in a direction to suppress a state quantity corresponding to the component with the second largest absolute value among the components of the eigenvector selected in step S2, an intervention step S5 intervenes in the network in a direction to promote a state quantity corresponding to the second largest component among the components of the eigenvector selected in estimation step S2. When the fluctuation of the network is still not suppressed, an intervention step S5 intervenes in the network in a direction to suppress a state quantity corresponding to the component with the third largest absolute value among the components of the eigenvector selected in estimation step S2.

[0098] Similarly, if the network fluctuation is not suppressed even after intervention in the suppression direction, intervention in the promotion direction is performed in the intervention step S5. If the network fluctuation is still not suppressed, intervention step S5 intervenes in the direction of suppressing the state quantity corresponding to the component with the next largest absolute value among the components of the eigenvector selected in step S2. Intervention step S5 repeats the above processing procedure until the network fluctuation is suppressed.

[0099] According to this embodiment, fluctuations in the target network can be suppressed with even higher accuracy.

[0100] [Verification experiment] The inventors conducted an experiment to verify the effectiveness of the technique of the present disclosure. (Experiment 1) Experiment 1 is a numerical simulation. Figure 9 shows the network structure used in the simulation. This network was generated using the Holme-Kim model and has scale-free properties and high clustering. There are 20 nodes. Each node has a self-loop with a probability of 0.1.

[0101] Figure 10 shows the state of each node in the network. The horizontal axis represents the calculation steps in 10 steps. 5 The bifurcation parameter γ is expressed in units of 1.329. The state is healthy up to 1.329, but when this changes to 1.33, the state suddenly becomes ill. In other words, a bifurcation phenomenon occurs here. A sample of the state quantity is taken from the steady state just before the bifurcation. Here, the number of samples is set to 5.

[0102] FIG. 11(a) shows the values ​​of each component of the dominant right eigenvector. This figure shows the results based on the sample covariance matrix of five samples, the results based on the covariance matrix for all samples (20 samples), and the true value. The results based on the covariance matrix for all samples (20 samples) and the true value are in excellent agreement. Both the results based on the sample covariance matrix of five samples and the true value are generally in good agreement, although there are some discrepancies here and there. This shows that the technique disclosed herein can correctly estimate the dominant right eigenvector. Both results show that the contribution of the sixth gene is dominant.

[0103] Figure 11(b) shows the values ​​of each component of the dominant left eigenvector. As mentioned above, the dominant left eigenvector cannot be estimated, so only the true value is shown. As shown in the figure, it can be seen that the contribution of the 10th gene is dominant.

[0104] 12 is a diagram showing the product of the dominant right eigenvector and the dominant left eigenvector. From this, it is considered that the contributions of the sixth and tenth genes are ultimately dominant, and that network fluctuations can be suppressed by suppressing these genes.

[0105] (Experiment 2) In Experiment 2, colitis was induced in male BALB / c mice by allowing them to freely drink 3% dextran sulfate sodium (DSS) (MW: 36-50 kDa) (MP Biomedicals) for 7 days. Gene expression profiles of mouse colonic tissues were comprehensively analyzed using microarray analysis as described below, and these data were analyzed using dynamic network biomarker (DNB) theory (DNB analysis).

[0106] Microarray analysis was performed using the SurePrint G3 Mouse Gene Expression 8x60K Microarray Kit (Agilent Technologies). Colonic tissues were isolated from mice 0, 1, 3, 5, and 7 days after the start of DSS drinking (n = 5 for each time point), and total RNA extracted from the colonic tissue was used for microarray analysis. Microarray analysis was performed according to the kit's protocol.

[0107] In this experiment, DNB analysis was performed by first selecting genes with significantly altered expression levels from all genes using the gene expression data obtained from the microarray analysis of mouse colon tissue. The correlation coefficients between the expression levels of the selected genes were then calculated. Subsequently, genes with high correlations among the selected genes were clustered. As a result, 27 DNB genes were detected: Mcpt1, Mcpt4, Ifit2, Cd274, Trim30d, Tnfsf10, Ccn1, Wars, Tap2, Plppr3, Ube2l6, Bst2, Cxcl16, B2m, 4933412E12Rik, H2-T23, Znfx1, H2-M2, H2-Bl, H2-Q2, Gm11127, H2-K2, H2-Q8, H2-Q7, H2-Q6, H2-D1, and Fbxo6.

[0108] The 27 genes detected by the DNB analysis were scored using the method disclosed herein. Specifically, from the expression level data of all target genes, only the expression level data of the DNB gene on day 3 was extracted, and the eigenvector for the largest eigenvalue of the covariance matrix of that data was calculated. The components of this eigenvector were sorted in descending order of absolute value. After dividing each value by the maximum value, the proportion of variation related to the largest eigenvalue that explains the variance of the entire data was calculated and multiplied. The results are shown in Table 1.

[0109] Table 1 [Table 1]

[0110] Of the genes listed in Table 1, Mcpt1 and Mcpt4 are not present in humans, Ifit2, Cd274, and Tnfsf10 have been detected in conventional analyses using the average gene expression level as an indicator, while Trim30d, Ccn1, Plppr3, 4933412E12Rik, H2-T23, H2-M2, H2-Bl, H2-Q2, Gm11127, H2-K2, H2-Q8, H2-Q7, H2-Q6, and H2-D1 are not present in the above IBD data. Therefore, the present inventors focused on Wars among the genes listed in Table 1 and investigated whether it is a pathophysiologically significant gene in IBD below. Wars is also present in humans, but was not detected in conventional analyses using the average gene expression level as an indicator. It was first detected by DNB analysis and was a highly ranked gene.

[0111] (Experiment 3) Experiment 3 was an experiment to analyze the effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression. The effects of WRS recombinant protein and anti-WRS antibody on DNB gene expression were analyzed by real-time PCR using the following procedure.

[0112] A mouse model of DSS-induced colitis was generated by administering recombinant WRS protein or anti-WRS antibody as follows. Recombinant WRS protein (rWRS; CLOUD-CLONE) was dissolved in saline and administered intraperitoneally at 20 μg per mouse once daily on days 0, 2, 4, and 6 after the start of DSS drinking. Vehicle (saline) was administered as a control in the same manner. Anti-WRS antibody (Anti-WRS Ab) was generated using Cosmo Bio's first antibody and administered intraperitoneally at 150 μg per mouse once daily on days 0 and 2 after the start of DSS drinking. A control IgG antibody (rabbit IgG control (R&D Systems; catalog number: AB-105-C)) was administered in the same manner. Three days after the start of DSS drinking, real-time PCR was performed to analyze the expression levels of B2m, Bst2, Ccn1, Cd274, Cxcl16, Fbxo6, H2-D1, H2-K2, H2-M2, H2-Q2, H2-Q6, H2-Q7, H2-T23, Ifit2, Mcpt1, Mcpt4, Tap2, Trim30d, Ube2l6, Wars, and Znfx1.

[0113] For real-time PCR, RNA was extracted from the colon tissue using Sepasol RNA I Super G (Nacalai Tesque) according to the manufacturer's protocol, and the RNA concentration and quality were measured using Nano Drop (ND-1000; Thermo Fisher Scientific). Reverse transcription was performed to synthesize cDNA from the extracted RNA using the PrimeScript RT reagent Kit (Takara Bio).

[0114] Using the synthesized cDNA as a template, the expression levels of the target genes were measured using TB Green Premix Ex Tag (manufactured by Takara Bio Inc.). The expression levels of each target gene were normalized with the expression level of the TBP (TATA binding protein) gene, which serves as an internal standard. -ΔΔCtThe calculation was performed by the method described below. The primer combinations for each target gene listed in Table 2 were used to amplify the target gene and TBP gene. Primers for each target gene were purchased from Takara Bio Inc. As a control, normal BALB / c mice were also analyzed by real-time PCR for the expression of the genes listed in Table 2 below. The results are shown in Figures 13 to 18.

[0115] Table 2 [Table 2]

[0116] As shown in Figures 13 to 18, administration of WRS recombinant protein to colitis model mice suppressed fluctuations in the expression of Wars, as well as B2m, Cxcl16, and Ube2l6 in the pre-disease state (3 days after the start of DSS drinking).

[0117] The present invention has been described above based on the embodiments. These embodiments are merely examples, and it will be understood by those skilled in the art that various modifications are possible in the combination of each component and each treatment process, and that such modifications are also within the scope of the present invention.

[0118] When understanding the abstract technical ideas of the embodiments and modifications, the technical ideas should not be interpreted as being limited to the contents of the embodiments and modifications. The above-described embodiments and modifications are merely illustrative examples, and many design modifications, such as changes, additions, and deletions of components, are possible. In the embodiments, the contents in which such design modifications are possible are emphasized by adding the notation "embodiment." However, design modifications are also permitted even in contents without such notation. [Industrial Applicability]

[0119] The technology disclosed herein can be widely used for early responses to changes in natural and social phenomena, such as early treatment of diseases, early measures to deal with natural disasters and environmental changes such as earthquakes and climate change, early measures to deal with traffic congestion, early measures to deal with fluctuations in electricity demand, and early measures to deal with fluctuations in exchange rates and stock prices. [Explanation of symbols]

[0120] 1...intervention device, 2...intervention device, 11. State sample acquisition unit, 12...estimation section, 13...Intervention Department, 14··Control unit, S1: A step of taking a sample of the state quantity. S2: Estimating the dominant right eigenvector; S3: A step of suppressing the state variable corresponding to the component with the largest absolute value. S4: Determine whether the fluctuations are suppressed. S5: A step of implementing a promotional intervention on the state quantity corresponding to the component with the largest absolute value. S6: determining whether fluctuations have been suppressed; S7: A step of implementing an inhibitory intervention on the state quantity corresponding to the component with the second largest absolute value.

Claims

1. An intervention device for suppressing fluctuations in a network in which nodes having state quantities are connected to each other, a state quantity sample acquisition unit that acquires a plurality of samples of the state quantity; an estimation unit; The intervention department and A control unit; Equipped with the estimation unit selects an eigenvector related to the eigenvalues ​​of the covariance matrix of the acquired samples as an estimate of a dominant right eigenvector; an intervention device, characterized in that the pre-control unit controls the intervention unit to intervene in the network in a direction to suppress a state quantity corresponding to a component of an eigenvector related to the selected eigenvalue.

2. 2. The intervention device according to claim 1, wherein the control unit controls the intervention unit so that, when fluctuations in the network are not suppressed, the intervention unit intervenes in the network in a direction that promotes a state quantity corresponding to a component of the selected eigenvector.

3. 3. The intervention device according to claim 1, wherein the estimation unit selects an eigenvector associated with a largest eigenvalue among the eigenvalues ​​of the covariance matrix of the acquired samples as an estimate of a dominant right eigenvector.

4. 4. The intervention device according to claim 3, wherein the control unit controls the intervention unit to intervene in the network with a state quantity corresponding to a component with a largest absolute value among components of an eigenvector related to the selected largest eigenvalue.

5. 3. The intervention device according to claim 1, wherein the control unit controls the intervention unit so that, when fluctuations in the network are not suppressed, the intervention unit intervenes in the network in a direction to suppress a state quantity corresponding to a component different from a component of the selected eigenvector.

6. 2. The intervention device according to claim 1, wherein the network is a biological network in which genes are connected to each other.

7. 7. The intervention device according to claim 6, wherein the state quantity is an expression level of mRNA of the gene.

8. An intervention method for suppressing fluctuations in a network in which nodes having state quantities are connected to each other, comprising: a state quantity sample acquisition step of acquiring a plurality of samples of the state quantity; an estimation step; Intervention steps and Including, the estimating step selects an eigenvector related to the eigenvalues ​​of the covariance matrix of the acquired samples as an estimate of a dominant right eigenvector; The method is characterized in that the intervention step involves performing an intervention on the network in a direction that suppresses a state quantity corresponding to a component of the selected eigenvector.

9. 9. The method according to claim 8, wherein when the fluctuations of the network are not suppressed, the intervention step performs an intervention on the network in a direction that promotes a state quantity corresponding to a component of the selected eigenvector.

10. 10. The method according to claim 8, wherein the estimation step selects an eigenvector associated with a largest eigenvalue among the eigenvalues ​​of the covariance matrix of the acquired samples as an estimate of a dominant right eigenvector.

11. 11. The method according to claim 10, wherein the intervention step performs intervention on a state quantity corresponding to a component with the largest absolute value among components of an eigenvector related to the selected largest eigenvalue in the network.

12. 11. The method according to claim 10, wherein when the fluctuations of the network are not suppressed, the intervention step performs an intervention on the network in a direction to suppress a state quantity corresponding to a component other than a component of an eigenvector related to the selected largest eigenvalue.

13. A program for suppressing fluctuations in a network in which nodes having state quantities are connected to each other, a state quantity sample acquisition step of acquiring a plurality of samples of the state quantity; an estimation step; Intervention steps and Including, the estimating step selects an eigenvector related to the eigenvalues ​​of the covariance matrix of the acquired samples as an estimate of a dominant right eigenvector; The intervening step is a program that causes a computer to execute a method for intervening in the network in a direction that suppresses a state quantity corresponding to a component of the selected eigenvector.

14. 14. The program according to claim 13, wherein the intervention step causes a computer to execute a method of intervening in the network in a direction that promotes a state quantity corresponding to a component of the selected eigenvector when the fluctuation of the network is not suppressed.

15. 14. The program according to claim 13, wherein the intervention step causes a computer to execute a method of intervening in the network in a direction to suppress a state quantity corresponding to a component different from the selected component of the eigenvector when the fluctuation of the network is not suppressed.

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