KR20210021790A - A control method for driving any state of a Boolean network to a boundary state of the basin of a desired attractor by using a minimum temporary perturbation - Google Patents

Abstract

Disclosed is a method for determining a control node of a Boolean network. The method comprises the steps of: determining a boundary state of a desired first attractor basin not including an initial state from the initial state of a Boolean network; and determining, as a control node, nodes having different states when comparing the boundary state and the initial state among nodes of the Boolean network with each other. The boundary state is a state having a minimum Hamming distance among Hamming distances between the initial state and each state belonging to the first attractor basin among the states belonging to the first attractor basin.

Description

A control method for driving any state of a Boolean network to a boundary state of the basin of a desired attractor by using a minimum temporary perturbation}

The present invention relates to a control technique for sending a state of a Boolean network to a boundary state of a draw basin of a desired attraction using a minimum temporary perturbation, and to a technique that can be implemented by a computing device.

In order to change the state of cells in an undesired initial state (ex: cancer state) to a desired state (ex: cell death state), one type of drug or a combination of several types of drugs may be administered to the cells. At this time, if the same effect can be obtained by administering fewer drugs, it may be more preferable in terms of cost and minimization of drug side effects.

Changes in the phenotype of cells can be modeled and analyzed by a biomolecule signal processing network. In addition, the biomolecule signal processing network may be modeled as a Boolean network. Each node of the Boolean network may correspond to each molecule represented by the biomolecule signal processing network. Korean Patent Publication No. 10-2014-0032070 discloses a Boolean network and a state transition diagram.

It is an analysis method that can grasp the dynamics of the system at a glance along with a state transition diagram and a technique called attractor landscape used with it. Using the state transition diagram, all state transition paths of the system can be identified, and the attractor and its basin can be identified through the terrain of the attraction.

In the prior art for finding a catch basin of a specific attraction of a'boolean network', a state transition path to the specific attraction is calculated by applying a given update rule in all states that the system can have and converged to the specific attraction. Using the process of finding the state transition path, a state transition diagram of the entire specific attraction basin is obtained.

The above-described contents are described based on the contents known or researched by the inventors of the present invention in order to help the understanding of the present invention. Therefore, it should not be taken for granted that the above-described contents have been disclosed to an unspecified person prior to filing the patent application of the present invention.

In the present invention, it is intended to provide a technique that enables the combination of drugs to be administered to cells to be determined in order to change the state of the cells in an undesired initial state to a desired state.

In the present invention, it is intended to provide a technology for determining a protein to be controlled in order to change the state of a cell.

In the present invention, when a biomolecule signal processing network modeling a cell's dynamic system is modeled as a boolean network, a technology for determining a node that needs to control the state in order to change an undesired initial state of the Boolean network to a desired state I want to provide. At this time, each node of the Boolean network may represent a protein of a cell.

Some terms used in the present invention may be defined as follows.

-State: In the case of a Boolean network, each node has a value of 0 or 1, and the'state' of a Boolean network can be expressed as an ordered pair of all node values. According to this, when the total number of nodes in the Boolean network is N, the number of possible states is 2 ^N. The Boolean network may have a specific state at a specific moment, and the state of the Boolean network may change or remain unchanged over time.

-Attractor: Among the states of a Boolean network, a set of states that repeat over time can be referred to as a'attractor'. In the case of a life system, the attractor may correspond to a'phenotype' which means a state such as cancer or cell death.

-State transition trajectory: A path in which the state of a Boolean network changes over time without external interference may be referred to as a'state transition path'. When the state transition path is schematically expressed, an arrow can be drawn from a state at a specific past point in time to a state at a specific future point of the Boolean network. One state transition path may be represented by a plurality of states that change over time and arrows connecting the plurality of states.

-Basin: A collection of all states included on all state transition paths to a specific basin can be referred to as a basin. All the states included in the specific draw basin may converge to the state of the particular draw basin over time.

-Terminal state: A state that does not have a past state on a given state transition path can be referred to as a'terminal state'. In a given state transition path indicated by arrows, a state in which no arrows are directed may be regarded as the terminal state. The arrow connected to the terminal state starts from the terminal state.

-Hamming distance: The number of nodes whose values differ between the two states may be referred to as a'hamming distance' between the two states. For example, when the total number of nodes in the Boolean network is N, the number of nodes having different values is determined when comparing the first state and the second state among states specified by a combination of values of the N nodes. It may be referred to as a Hamming distance between the first state and the second state. As a specific example, when N=3, the first state is '101' and the second state is '100', the hamming distance between the first state and the second state is 1. As another example, when N=3, the first state is '101' and the second state is '010', the hamming distance between the first state and the second state is 3. In an embodiment of the present invention, the hamming distance may be regarded as the number of control nodes required for temporary control.

-Boundary: Among the states of the desired first draw basin [DB], the state at the shortest hamming distance from the unwanted second state [US] included in the second unwanted draw basin [UB] is called the'boundary state. ', or may be referred to as'the boundary state of the desired first drag basin [DB] from the undesired second state [US].'. The desired first claw basin [DB from the unwanted second state [US]] There can be one or more boundary states of ]. The set of boundary states may be referred to as'boundary' or'the boundary of the desired first drag basin [DB] from the undesired second state [US]."

'D' indicated in [] described in the present specification may mean'desired','U' may mean'undesired', and'B' may mean'Desired' It may mean'(basin)', and'S' can mean'state'.

-Control purpose: Optimally transitioning the state of the system from the unwanted second state [US] to the desired first drawer through temporary perturbation may be defined as a'control purpose' according to an embodiment of the present invention. Here, the second state [US] may be a state belonging to the second draw basin [UB], which is an unwanted second draw basin in the system. And the first drawer may be in a desired drawer state of the system. Here, transitioning to'optimal' may mean temporarily adjusting a minimum node value in order to transition from the undesired second state [US] to the boundary of the desired first draw basin [DB]. For example, in the case where the values of at least two nodes need to be adjusted to transition to the boundary of the desired first draw basin [DB], the transition is optimally performed if only the values of the two nodes are adjusted. Adjusting the values does not make the transition optimal.

-Temporary perturbation: Temporarily changing the value of a node may be referred to as'temporary perturbation'. If the perturbation is stopped immediately after temporarily changing the value of one or more nodes, the state of the Boolean network changes according to its inherent dynamics. In one embodiment of the present invention, the node to be controlled is temporarily perturbed, but in the comparative embodiment, the value of the node to be controlled may be perturbed by forcibly continuously fixing the value. According to this comparative example, since the value of a specific node is forcibly fixed continuously, the Boolean network may not behave according to its inherent dynamics.

-Initial state: In the present invention, as a state in which temporary perturbation needs to be provided or temporary perturbation needs to be applied, for example, an undesired second state [US] belonging to an undesired second drag basin [UB] is' It can also be referred to as'initial state'. According to this, the boundary state may be referred to as "the boundary state of the desired first drag basin [DB] from the initial state".

-Symmetrical nodes: Symmetrical nodes can be classified into two types. First,'Structural Symmetry Node' is a symmetric node determined only from the network structure, and is always a symmetric node in all draw basins. Second, the'dynamic symmetric node' is an additional symmetric node that appears according to the dynamic characteristics of each attraction in addition to the structural symmetric node, and the structural symmetric node can be known without calculating the attraction basin, but the dynamic symmetric node calculates a specific attraction basin. You will know only after you have done it.

A node without an outgoing link in the network structure can be considered as a'structural symmetric node'. In addition, when there is only one outgoing link and a node connected to the outgoing link is a structurally symmetrical node, the node may also be regarded as a structurally symmetrical node.

As an example of the specific meaning of'symmetry', let N=3, nodes are A, B, and C, and node A is a structurally symmetrical node found from the network structure. If there is a state (A, B, C) = (0, b, c) in a particular draw basin, then the state (A, B, C) = (1, b, c) must exist in the draw basin. Since node A causes this symmetry, it can be referred to as a symmetric node.

Alternatively, there may be nodes that are not structurally symmetrical nodes but satisfy the symmetry described in the above examples (N=3, nodes A, B, C) when calculating the draw basin of a specific draw. Since it is a symmetric node that can be found after calculating the draw basin, it can be referred to as a'dynamic symmetric node'.

-Fixed node: A node whose value is always constant in all states of a specific draw basin can be defined as a fixed node.

According to an embodiment of the present invention, in order to achieve the above control object, the state is transitioned from an undesired initial state to a desired boundary by a temporary perturbation.

According to an aspect of the present invention, from an initial state of a Boolean network, determining a boundary state of a desired first draw basin that does not include the initial state; And determining, as a control node, nodes having different states of the boundary state and the initial state among the nodes of the boolean network as a control node, wherein the boundary state is among states belonging to the first drag basin. , A method for determining a control node of a Boolean network, characterized in that the initial state has a minimum hamming distance among hamming distances between the states belonging to the first draw basin.

In this case, the method of determining a control node of the Boolean network may further include perturbing the control node among nodes of the Boolean network in the initial state.

At this time, the perturbation of the control node may be performed only temporarily.

In this case, the determining of the boundary state may include determining a symmetric node among nodes of the boolean network (the symmetric node has an average value of 0.5 when the values of the states of the Boolean network are averaged for each node, , Nodes in which the state of the draw basin except for the node is symmetrical); Determining a fixed node among the nodes of the Boolean network (the fixed node is a node whose value is always constant in all states of the first draw basin); Calculating a partial hamming distance between the initial state and each state included in the first draw basin (the partial hamming distance is for only non-fixed/asymmetric nodes, which are nodes excluding the symmetric node and the fixed node) Calculated hamming distance); And determining a state having a minimum distance among the partial hamming distances between the initial state and the respective states belonging to the first claw basin, among states belonging to the first claw basin, as the boundary state. It may include.

In this case, the boolean network is a model of a biomolecule signaling network, and each node of the boolean network may correspond to each molecule of the biomolecule signaling network.

In this case, the step of determining the boundary state includes a fixed node determination step of determining a fixed node, which is defined as a node whose value is always constant in all states of the first draw basin among the nodes of the boolean network. ; A hamming distance calculation step of calculating a hamming distance between the initial state and each state included in the first draw basin; And determining a state having a minimum Hamming distance from the initial state among states belonging to the first drag basin as a boundary state. In this case, the hamming distance may be a hamming distance between the initial state and each state included in the first drag basin, calculated by targeting only nodes other than the fixed node among the nodes of the Boolean network.

In this case, the step of calculating the hamming distance further includes calculating a partial hamming distance between the initial state and each state included in the first claw basin, wherein the partial hamming distance is the symmetric node and the fixed node It is a hamming distance calculated for only non-fixed nodes and asymmetric nodes, which are nodes except for, and determining that the boundary state is, among states belonging to the first draw basin, the initial state and the first drawer It may include the step of determining a state having a minimum distance among the partial hamming distances between the states belonging to the watershed as the boundary state.

In this case, the method for determining a control node of the Boolean network may further include determining a symmetric node among nodes of the Boolean network. At this time, the symmetric node includes a structural symmetric node defined as a node that does not have an outgoing link in the structure of the Boolean network, and the hamming distance is the fixed node and the symmetric node among nodes of the boolean network. It may be a Hamming distance between the initial state and each state included in the first drag basin, calculated by targeting only the excluded nodes.

In this case, the symmetric node has only one outgoing link in the structure of the Boolean network, and a node connected to the outgoing link may further include another structural symmetric node, which is the structural symmetric node.

At this time, the symmetric node further includes a dynamic symmetric node defined as a node whose average value is 0.5 when the values of the states of the Boolean network are averaged for each node, and the remaining states are symmetrical based on the node. can do.

In this case, the method for determining a control node of the Boolean network may further include determining a symmetric node among nodes of the Boolean network. At this time, the symmetric node includes a dynamic symmetric node defined as a node in which the values of the states of the Boolean network are averaged for each node, and the average value is 0.5, and the remaining states are symmetrical based on the node. , The hamming distance may be a hamming distance between the initial state and each state included in the first draw basin, calculated for only nodes other than the fixed node and the symmetric node among the nodes of the Boolean network. have.

In this case, the method of determining all the states belonging to the first claw basin may include: acquiring information on the first claw basin belonging to the first claw basin; Initializing the reference state of the boolean network to the first draw; And ① a first update rule, which is an update rule of the state of the boolean network, and ② a state backtracking step of calculating a state immediately before the Boolean network based on the reference state of the Boolean network, wherein the reference state is a reference point Is defined as a state of the Boolean network at, and the immediately preceding state may include the state backtracking step, which is defined as a state of the Boolean network at a point immediately preceding the point of time immediately before the reference point. At this time, for each of the calculated immediately preceding states, by repeating the state backtracking step after updating the reference state to the calculated immediately preceding state, all states of the first dragged basin including the first dragged were determined. I can.

At this time, for those determined to be the terminal state among the calculated immediately preceding states, the qualification as the state of the first network at the reference point is not granted, and the state backtracking step is not repeated. The terminal state may be a state in which a previous state does not exist on the state transition path including the terminal state.

At this time, the boolean network is a symmetric node from which the symmetric node has been removed from the first Boolean network, and the first draw of the boolean network is a value of the removed symmetric node from a specific draw of the first Boolean network. I can.

According to another aspect of the present invention, a computing device including a communication interface and a processing unit for communicating with an external device by wire or wirelessly may be provided. In this case, the processing unit includes information on the structure of the Boolean network from the external device through the communication interface, information on the initial state of the Boolean network, and the initial state among attractors of the Boolean network. It is intended to obtain information on the first drag basin belonging to the desired first basin, and to determine the boundary state of the first basin from the initial state, and the boundary state among nodes of the boolean network Among the initial states, nodes having different states are determined as control nodes. In this case, the boundary state is a state having a minimum hamming distance among hamming distances between the initial state and respective states belonging to the first claw basin among states belonging to the first claw basin.

According to another aspect of the present invention, the processing unit of a computing device including a communication interface and a processing unit that communicates with an external device by wire or wirelessly causes information on the structure of a Boolean network from the external device through the communication interface. And acquiring information on an initial state of the boolean network and information on a first attraction in a desired first attraction basin that does not include the initial state among attraction of the Boolean network; Determining a boundary state of the first drag basin from the initial state; And a computer-readable non-transitory storage device in which a program for executing the step of determining, as a control node, nodes having different states of the boundary state and the initial state among the nodes of the Boolean network. I can. In this case, the boundary state is a state having a minimum hamming distance among hamming distances between the initial state and respective states belonging to the first claw basin among states belonging to the first claw basin.

According to the present invention, a technique capable of determining a combination of drugs to be administered to a cell may be provided in order to change the state of a cell in an undesired initial state to a desired state.

An object of the present invention is to provide a technology for determining a protein to be controlled in order to change the state of a cell.

According to the present invention, when a biomolecule signal processing network modeling a cell's dynamic system is modeled as a boolean network, the node that needs to control the state is determined in order to change the unwanted initial state of the Boolean network to a desired state. Skills can be provided.

1 is a first state transition path and the first state transition path showing a series of states in a process of changing over time from a first terminal state to a specific attraction in a specific attraction basin of a given first boolean network. It shows the concept of the first station-state transition path, which is a path that goes back in time.
2 shows an example of a network structure of a first boolean network.
FIG. 3 shows a first sub-network obtained by removing a structurally symmetric node from the first boolean network shown in FIG. 2.
FIG. 4 is a representation of a node classified as a crystalline node in FIG. 3 in a square shape.
5 shows the values of each node at the immediately preceding point among the values of each node of the first sub-network on the left side, and the values of each node at the reference point immediately after the immediately preceding point on the right side. It is a schematic diagram of which node the value of each node is affected by.
6 is a flowchart illustrating a method of determining whether a specific state of a given first boolean network is a terminal state, according to an embodiment of the present invention.
7 is a flowchart illustrating a method of determining all states of a specific draw basin to which a particular draw of a given first Boolean network belongs, according to an embodiment of the present invention.
8 is a diagram to help understand some terms used in an embodiment of the present invention.
9 is another diagram for explaining a terminal state, a boundary state, a minimum hamming distance, a hamming distance, a desired drawer, a drawer, an initial state, and a state transition path used in an embodiment of the present invention.
FIG. 10 is a further elaboration of the concept presented in FIG. 9, and shows each state as a combination of values of a plurality of nodes.
11 is a flowchart illustrating a method of determining a control node for changing a biomolecule signaling network modeled as a Boolean network to a desired state, that is, a method of determining a biomolecule serving as a control target according to an embodiment of the present invention. .
12 is a flowchart illustrating a method of determining a boundary state of a first drag basin from a specific initial state according to an embodiment of the present invention.
The graph shown in FIG. 13 shows the states of a draw basin of a specific draw in a network composed of 21 nodes, and is for explaining the properties of the above-described symmetric node.
14 shows another example of a p53 network for explaining the concept of an embodiment of the present invention.
15A is a diagram for explaining a control target according to an embodiment of the present invention.
15B is a list of states of fixed nodes and non-fixed/asymmetric nodes in an initial state and a first boundary.
15C is a list of states of fixed nodes and non-fixed/asymmetric nodes in the initial state and the second boundary.
16 is a diagram illustrating a computing device and devices communicating with the computing device provided according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, the present invention is not limited to the embodiments described in the present specification, and may be implemented in various different forms. The terms used in the present specification are intended to aid understanding of the embodiments, and are not intended to limit the scope of the present invention. In addition, the singular forms used below also include plural forms unless the phrases clearly indicate the opposite meaning.

I. A method for quickly determining all conditions of a specific draw basin according to an embodiment of the present invention

1 is a first state transition path representing a series of states in the process of changing over time from a first terminal state 1111 to a specific drawer 1131 in a specific draw basin of a given first boolean network ( 3101) and the concept of a first inverse-state transition path R3101, which is a path that goes back in time through the first state transition path.

In FIG. 1, the closed curve indicated by the dotted line shows the terminal states among the states of the specific attraction basin.

In an embodiment of the present invention, by calculating all inverse-state transition paths starting from the specific attractor 1131, reversing the passage of time from the specific attractor 1131, on the premise that the value of the specific attractor 1131 can be known. It is possible to determine the values of all states of the specific draw basin.

In step S11 according to an embodiment of the present invention, a network structure of a given first boolean network may be obtained.

2 shows an example of the network structure of the first boolean network presented in step S11. The example shown in FIG. 2 shows an example of a simple structure to aid understanding of the present invention.

In step S12 according to an embodiment of the present invention, a structurally symmetric node among the first boolean network may be determined.

A method of determining the structurally symmetric node will be described later.

In the first boolean network illustrated in FIG. 2, the structural symmetric node is X ₅ .

In step S13 according to an embodiment of the present invention, a first sub-network obtained by removing all the determined structurally symmetric nodes from the structure of the first boolean network is determined.

FIG. 3 shows a first sub-network obtained by removing the structurally symmetric node from the first boolean network shown in FIG. 2.

In step S14 according to an embodiment of the present invention, a first update rule, which is an update rule of the state of the first sub-network, may be determined based on information on the structure of the first sub-network.

For example, the first update rule may be given as the following equations 1 to 4 without the _{structural symmetry node X 5.} Each of Equations 1 through 4 has two sides. The left side represents the state of each node at the reference point (= future point), and the right side represents the state of each node at the point immediately preceding the reference point (= past point).

Here, the state of the sub-network at the immediately preceding point of time is changed to the state of the sub-network at the reference point of time without going through any other state. That is, the immediately preceding point is a point immediately preceding the reference point.

[Equation 1] X ₁ ^* =X ₃ ∨￢X ₄

[Equation 2] X ₂ ^* =X ₁

[Equation 3] X ₃ ^* =￢X ₂

[Equation 4] X ₄ ^* =￢X ₁

In step (S21) according to an embodiment of the present invention, from the first update rule or from information on the structure of the first sub-network, the state at the point immediately preceding (= past point) of the first node is the It is determined whether or not it is uniquely determined by the state at the reference point (= future point) of the first sub-network, and if it is uniquely determined, the first node is classified as a crystalline node, and if it is not uniquely determined, The first node may be classified as an amorphous node.

In Equations 1 to 4, _{it can be seen that the state at the point immediately preceding the node X 1} and the node X ₂ is uniquely determined by the state at the reference point immediately after it. Therefore, node X ₁ and node X ₂ are classified as the above crystalline nodes.

From Equations 1 to 4, it can be seen that the state at the point immediately preceding the _{node X 3} and the node X _{4 is not uniquely determined by the state at the reference point.} Accordingly, node X ₃ and node X ₄ are classified as the amorphous nodes.

FIG. 4 is a representation of a node classified as a crystalline node in FIG. 3 in a square shape.

In step S22 according to an embodiment of the present invention, a node having a plurality of outbound links among the nodes classified as the crystalline node may be classified as a discrimination node.

Referring to the structure of the first sub-network shown in FIG. 3, two outbound links from _{node X 1} among the crystalline nodes are plural, and one outbound link from _{node X 2 among the crystalline nodes is 1} As a dog, it is not a plurality of dogs. Therefore, in the case of the first sub-network shown in FIG. 3, the determination node is node X ₁ .

5 shows the values of each node at the immediately preceding point among the values of each node of the first sub-network on the left side, and the values of each node at the reference point immediately after the immediately preceding point on the right side. It is a schematic diagram of which node the value of each node is affected by. The structure of FIG. 5 can be easily understood from the link of FIG. 3 or 4.

When a sub-network according to another example is given, there may be no or multiple discrimination nodes.

The first renewal rule may be re-presented by Equations 5 to 8 below. Equations 5 to 8 below may also be regarded as the first update rule.

[Equation 5] X ₃ ∨￢X ₄ =X ₁ ^*

[Equation 6] X ₁ =X ₂ ^*

[Equation 7] ￢X ₂ =X ₃ ^*

[Equation 8] ￢X ₁ =X ₄ ^*

The first renewal rule may be presented again in Equations 9 to 12 below. Equations 9 to 12 below may also be regarded as the first update rule.

[Equation 9] X ₃ ∨￢X ₄ =X ₁ ^*

[Equation 10] X ₁ =X ₂ ^*

[Equation 11] X ₂ =￢X ₃ ^*

[Equation 12] X ₁ =￢X ₄ ^*

In step (S23) according to an embodiment of the present invention, among both sides of each equation (Equation 1 to Equation 4, or Equation 5 to Equation 8, or Equation 9 to Equation 12) included in the first update rule It can be checked whether the discrimination node is included in the first side representing the past state (= the previous state), which is the state of the sub-network.

For example, in Equations 9 to 12, the first side representing the past state at the time immediately preceding is the left side of the left side and the right side.

In step S24 according to an embodiment of the present invention, among the equations included in the first update rule, equations in which the discrimination node is included on the first side may be selected.

For example, in the example of step S22, the discrimination node is node X ₁ , and in equations 9 to 12, _{equations including node X 1} on the left side are equations 10 and 12. Thus, the selected equations are equations 10 and 12.

Using the selected equations in step S25 according to an embodiment of the present invention, a discriminant for determining whether the state of the sub-network at a reference point, which is a point immediately following the point in time, is the above-described terminal state. You can decide.

For example, as for the selected equation, looking at equations 10 and 12, in order for a valid past state _{value of X 1} to exist, a relationship of X ₁ =X ₂ ^* =X ₁ =￢X ₄ ^* must be established. That is, only when the relationship of _{X 2} ^* =￢X ₄ ^* _{is established, X 1, which} is the immediately preceding value of the _{given X 1} ^* , can exist in effect.

Conversely if the ten thousand and one X ₂ ^* = ¬X ₄ ^* not in the relationship established, i.e., X ₂ ^* = X ₄ ^* If the relation is established, the view of X ₁ is given immediately before the value of X ₁ ^* it does not exist, effectively I can. _{That is, if a state in which a relationship of X 2} ^* =X ₄ ^* is established among the possible states of the first sub-network is given, it can be seen that there is no state of another value that occurred before the given state. And by the above definition, the given state may be regarded as a terminal state.

At this time, above The _{formula defined by X 2} ^* =X ₄ ^* can be defined as the above-described discriminant. Equation 13 below is a discriminant for determining whether a specific state can be obtained from the first sub-network or whether a specific state is a terminal state.

Depending on the structure of the sub-network, there may be no discriminant or a plurality of discriminants may exist.

[Equation 13] = [Equation] X ₂ ^* =X ₄ ^*

In step S31 according to an embodiment of the present invention, a specific attractor of the first boolean network may be obtained.

_{For example, values of each node (X 1} to X ₅ ) of the first boolean network in the specific drawer may be presented as shown in Tables 1 and 2 below. A time point having the state of Table 1 or Table 2 may be referred to as a first time point or a reference time point.

First state of the first boolean network at the reference point (example) X ₁ X ₂ X ₃ X ₄ X ₅ 0 One One 0 One

Second state of the first boolean network at the reference point (example) X ₁ X ₂ X ₃ X ₄ X ₅ One 0 0 One One

In step S32 according to an embodiment of the present invention, a first drawer of a first sub-network, which is a sub-network of the first boolean network, may be obtained.

For example, values of each node of the first sub-network in the first drawer may be presented as shown in Tables 3 and 4 below. A time point having the states of Tables 3 and 4 may be referred to as a first time point below.

In the present specification, the state of the first sub-network at the first point of view may be referred to as'the state of the reference point of view','the state of the first point of view' or'the state of the first layer'. When the first attraction is a point attractor, there may be one'state of the reference point of view' in the first attraction area, which is the area of attraction of the first attraction. In comparison, when the first drawer is a cyclic attractor, there may be a plurality of'states of the reference point of view' in the first drawer basin, which is the first drawer basin. Tables 3 and 4 show the case where the first drawer is a cyclic drawer.

The first state at the reference point (example) X ₁ X ₂ X ₃ X ₄ 0 One One 0

Second state at the reference point (example) X ₁ X ₂ X ₃ X ₄ One 0 0 One

In step (S41) according to an embodiment of the present invention, using ① the first drag value of the first sub-network and ② the first update rule, at a point immediately before the reference point (= second point) Any one of the states of the first sub-network may be calculated.

In the present specification, the state of the first sub-network at a second point of time that is a point immediately before the reference point may be referred to as a'state of the immediately preceding point of view','the state of the second point of view', or'the state of the second layer'. . There may be no, one, or a plurality of states of the immediately preceding point in time.

For example, in the first state {X ₁ , X ₂ , X ₃ , X ₄ } = {0, 1, 1, 0} shown in Table 3 ② immediately before the reference point by applying the update rule When one of the states at the time point, the'first state at the point of time immediately before' is calculated, it can be presented as shown in Table 5.

First state at the point immediately before (example) X ₁ X ₂ X ₃ X ₄ One 0 0 One

It can be seen that the first state shown in Table 5 is the same as the second state (= cyclic drawer) at the reference point. Therefore, it can be understood that depending on the nature of the cyclic drawer, the state at the third time point, which is a time point that occurs in advance than the immediately preceding time point, becomes the same as the first state at the reference time point.

_{By applying the update rule to the second state {X 1} , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1} at the reference point shown in Table 4, If another one of the states,'the second state at the point of time immediately before' is calculated, it can be presented as shown in Table 6.

Second state at the previous point (example) X ₁ X ₂ X ₃ X ₄ 0 One One 0

It can be seen that the second state shown in Table 6 is the same as the first state (= cyclic drawer) at the reference point. Accordingly, it can be understood that the state at the third time point, which is a time point that occurred earlier than the immediately preceding time point, becomes the same as the second state at the reference time point again.

_{By applying the update rule to the second state {X 1} , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1} at the reference point shown in Table 4, If another one of the states is calculated, the'third state immediately before' can be presented as shown in Table 7.

The third state at the previous point (example) X ₁ X ₂ X ₃ X ₄ 0 One One One

_{By applying the update rule to the second state {X 1} , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1} at the reference point shown in Table 4, If another one of the states,'the fourth state at the point of time immediately before' is calculated, it can be presented as shown in Table 8.

The third state at the previous point (example) X ₁ X ₂ X ₃ X ₄ 0 One 0 0

Summarizing the states presented in Tables 3 to 8 above, the state of the reference point (first layer or first point) is {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1 ,0} and {X ₁ , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}. And in the state of the immediately preceding view (2nd layer or 2nd view), {X ₁ , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}, {X ₁ , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}, {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1,1}, and {X ₁ , X ₂ , X ₃ , X It can be seen that there are _{4} = {0,1,0,0}.}

Now, it is possible to repeatedly calculate whether each of the four newly calculated states of the immediately preceding point has a previous state, which is the state of the previous point of time.

In this case, it is possible to check whether the terminal state exists among the four newly calculated states of the immediately preceding viewpoint using the discriminant. After such a check operation, it is not necessary to go through the process of obtaining the states of the previous state issued prior to the states of the immediately preceding point of time, for the states immediately before the terminal state, which is confirmed to be the terminal state, thus reducing the computing power. That is, the following step (S51) can be executed.

In step S51 according to an embodiment of the present invention, the state of the immediately preceding point that satisfies the discriminant among the states of the immediately preceding point newly calculated from the state of the reference point may be determined as the terminal state.

For example, the discriminant derived for the first sub-network is Equation 13, the states of the immediately preceding point {X ₁ , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}, {X ₁ , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}, {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1,1}, and {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,0,0}, which is the third state at the point immediately before {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1 Only ,1} satisfies the above discriminant. Therefore, it can be determined that only the third state at the point immediately preceding the terminal state is the terminal state.

In step (S61) according to an embodiment of the present invention, among the states of the immediately preceding point, the status as determined as ① not in the terminal state and ② not in the drawer (= the first drawer) is qualified as the state of the new reference point in time. And determine the state of the immediately preceding point for each of the states of the new reference point.

_{For example, among the four states immediately before, {X 1} , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}, {X ₁ , which was found to be a drawer (= first drawer). , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1} cannot be qualified as the state of the new reference point. In addition, among the four states immediately preceding, {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1,1}, which is found to be the terminal state, is qualified as the state of the new reference point. Cannot be given.

_{Therefore, only {X 1} , X ₂ , X ₃ , X ₄ } = {0,1,0,0} among the four states of the immediately preceding point of time cannot be qualified as the state of the new reference point.

Therefore, {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,0,0} can be used as the state of the reference point, and the state of the immediately preceding point of time may be generated according to the update rule.

By repeating the above-described steps, if a state that can be qualified as the state of the new reference point is no longer found, all of the first claw basins included in the first claw basin to which the first claw of the first sub-network belongs. It can be considered that the state has been determined.

In step S71 according to an embodiment of the present invention, by adding the value of the removed symmetric node to all the state values of the first draw basin, the specific drawer of the first Boolean network belongs. All conditions of a particular draw basin can be determined.

At this time, as the value of the symmetric node, all values that the symmetric node can have may be added. For example, when there is one symmetric node that has been removed, the number of all states of the specific draw basin of the first Boolean network may be twice the number of all states of the first draw basin of the first sub-network.

6 is a flowchart illustrating a method of determining whether a specific state of a given first boolean network is a terminal state, according to an embodiment of the present invention.

The network structure of the first boolean network given in step S11 may be obtained.

In step S12, a structurally symmetric node among the first boolean networks may be determined.

In step S13, a first sub-network obtained by removing all the determined structural symmetric nodes from the structure of the first boolean network is determined.

In step S14, a first update rule, which is an update rule of the state of the first sub-network, may be determined based on information on the structure of the first sub-network.

In step (S21), from the first update rule or from the information on the structure of the first sub-network, the state at the point immediately preceding (=the past point) of the first node is the reference point of the first sub-network ( =Future point) determines whether or not it is uniquely determined by the state, and if it is uniquely determined, the first node is classified as a crystalline node, and if it is not uniquely determined, the first node is an amorphous node. It can be classified as

In step S22, a node having a plurality of outbound links among the nodes classified as the crystalline node may be classified as a discrimination node.

In step S23, the past state, which is the state of the sub-network, among both sides of each equation (Equation 1 to Equation 4, or Equation 5 to Equation 8, or Equation 9 to Equation 12) included in the first update rule ( It is possible to check whether the discrimination node is included in the first side indicating =immediate state).

In step S24, among the equations included in the first update rule, equations in which the discrimination node is included in the first side may be selected.

Using the selected equations in step S25, a discriminant for determining whether the state of the sub-network at a reference point, which is a point immediately following the point of time immediately preceding, is the above-described terminal state may be determined.

7 is a flowchart illustrating a method of determining all states of a specific draw basin to which a particular draw of a given first Boolean network belongs, according to an embodiment of the present invention.

In step S31, a specific attractor of the first boolean network may be obtained.

In step S32, a first drawer of a first sub-network, which is a sub-network of the first boolean network, may be obtained.

In step S41, the state of the first sub-network at a point immediately before the reference point (= a second point) using the value of the first drag number of the first sub-network and ② the first update rule. Any one of these can be calculated.

In step S51, the state of the immediately preceding point that satisfies the discriminant among the states of the immediately preceding point newly calculated from the state of the reference point may be determined as the terminal state.

In step (S61), among the states of the immediately preceding point in time, the condition that is determined to be ① not in the terminal state and ② not in the drawer (= first drawer) is given a qualification as the state of the new reference point, and For each of the states, it is possible to determine the state of the previous point.

In step (S71), by adding the value of the removed symmetric node to all the determined state values of the first draw basin, determine all states of the specific draw basin to which the particular draw basin of the first Boolean network belongs. I can.

II. An application case that can be implemented using information on all states of a specific draw basin determined according to an embodiment of the present invention-A method of converting an unwanted initial state into a desired drawer

As described above, according to an embodiment of the present invention, even if the terrain of the boolean network is not completely known, it is possible to quickly determine all the states of the specific draw basin to which the desired specific draw of the boolean network belongs. Hereinafter, an application case that can be performed using all the states of the specific attraction basin determined in this way is presented.

According to an embodiment of the present invention, it is possible to provide a method of transitioning a state by temporary perturbation from an undesired initial state to a desired boundary.

8 is a diagram to help understand some terms used in an embodiment of the present invention.

Circles 1111, 1121, 1131, and 1211 shown in FIG. 8 represent different states classified by a combination of values of nodes of a Boolean network, respectively. The boolean network may be the first boolean network described in FIGS. 1 to 7 described above.

The states 1111, 1121, and 1131 are states belonging to the desired first drag basin [DB].

State 1211 is an undesired second state [US] 1211 belonging to the undesired second draw basin [UB]. That is, the state 1211 is the first initial state 1211, which is an initial state in which temporary perturbation needs to be provided or a temporary perturbation needs to be applied.

The states 1111, 1121, and 1131 are states that exist on the first state transition path 3101 among one or more state transition paths existing in the desired first drag basin [DB]. Other states not shown in FIG. 8 may further exist in the first state transition path 3101. The arrows displayed on the first state transition path 3101 indicate the direction of state change over time. The state on the first state transition path 3101 changes in the order of state (1111) -> state (1121) -> state (1131).

In particular, state 1111 represents a terminal state 1111 in which no previous state exists in the time domain, state 1121 represents a boundary state from an undesired state 1211, and state 1131 represents a desired state. The desired first attraction 1131 of the first attraction basin [DB] is shown.

Reference number 2101 denotes a set of states having the same hamming distance HD1 from the first initial state 1211 to the terminal state 1111, and reference number 2102 is the same as the first drawer 1131 from the first initial state 1211. A set of states having a Hamming distance HD2 is indicated, and reference numeral 2103 denotes a set of states having a minimum Hamming distance mHD, such as from the first initial state 1211 to the boundary state 1211. At this time, a relationship of mHD <HD1 <HD2 is established.

In FIG. 8, the boundary state 1121 of the first claw basin [DB] from the first initial state 1211 is present on the state transition path 3101, but the first claw basin [DB] is not shown. In another state transition path, the boundary state of the first drag basin [DB] from the first initial state 1211 may not exist.

9 is another diagram for explaining a terminal state, a boundary state, a minimum hamming distance, a hamming distance, a desired drawer, a drawer, an initial state, and a state transition path used in an embodiment of the present invention.

Reference numerals 3102, 3103, 3104, and 3105 denote different state transition paths included in the desired first drag basin [DB], respectively.

Reference numeral 1212 denotes a second initial state 1212, which is a state included in the undesired second draw basin [UB] and is an initial state in which temporary perturbation needs to be provided or temporary perturbation is to be applied.

Reference number 2201 denotes a first set of states having a hamming distance 2 from the second initial state 1212, and reference number 2202 denotes a second set of states having a hamming distance 3 from the second initial state 1212, Reference number 2203 denotes a third set of states having a hamming distance 4 from the second initial state 1212, and reference number 2204 denotes a fourth set of states having a hamming distance 5 from the second initial state 1212, Further, reference numeral 2206 denotes a sixth set [m] having a minimum hamming distance of 1 from the second initial state 1212. In the example shown in FIG. 9, terminal states 1112, 1113, 1114, and 1115 belong to the first set, the second set, the first set, and the first set, respectively. In the example shown in Fig. 9, the desired second drawer 1132 belongs to the fourth set. Further, the boundary states 1123 and 1125 all belong to the sixth set [m].

All of the circles shown in FIG. 9 except for the second initial state 1212 are included in the desired first drag basin [DB].

FIG. 10 is a further elaboration of the concept presented in FIG. 9, and shows each state as a combination of values of a plurality of nodes.

10A is an example of a given Boolean network 100. In (a) of FIG. 10, the circles surrounding English capital letters A, B, C, D, E, F, and G mean different nodes included in the boolean network 100. That is, the Boolean network 100 shown in FIG. 10A is defined by a total of 7 nodes and links connecting the nodes.

Fig. 10(b) is a schematic diagram of values of one state of the Boolean network shown in Fig. 10(a). In FIGS. 10B, 10C, and 10D, a set of 7 nodes attached to each other represents one state.

In (b) of FIG. 10, the node of the thin outline 101 represents the first binary value '1' of the binary values 0 and 1 that each node of the boolean network can have, and the node of the thick outline 102 is Represents the second binary value '0'. In the example of FIG. 10B, the node B and the node G have the second binary value, and the remaining nodes have the first binary value.

In FIG. 10C, the state 1133 represents the desired first drawer 1133. There are a plurality of state transition paths directed to the desired first drawer 1133, and these are denoted by reference numerals 3106, 3107, and 3108, respectively. In (c) of FIG. 10, it can be assumed that all states included in the desired first draw basin [DB], which is the desired first draw basin of the desired first draw basin 1133, can be known. Among them, only the desired first drawer 1133 and the terminal state 1116, which are some terminal states, are shown.

In (d) of FIG. 10, assuming that a second initial state 1213, which is an undesired state belonging to an undesired draw basin [UB], is given, the first draw basin from the second initial state 1213 The boundary status of [DB] (1126) can be found.

In the example shown in Fig. 10(d), the hamming distance HD between the second initial state 1213 and the desired first drawer 1133 is 4, and the second initial state 1213 and the boundary state ( The minimum hamming distance (mHD) between 1126) is set to be 1. In the example shown in FIG. 10D, the second initial state 1213 and the boundary state 1126 only differ from each other by the value of the node C. Therefore, if only the value of the node C in the second initial state 1213 is temporarily perturbed, that is, if it is temporarily changed, the state of the given Boolean network 100 belongs to the desired draw basin [DB]. 1126). As a result, the state of the given Boolean network 100 eventually reaches the desired state of the attractor 1133 along the state transition path to which the boundary state 1126 belongs.

According to the concept shown in FIG. 10, a method of determining a control node according to an embodiment of the present invention may be described as shown in the flowchart shown in FIG. 11.

11 is a flowchart illustrating a method of determining a control node for changing a biomolecule signaling network modeled as a boolean network to a desired state, that is, a method of determining a biomolecule serving as a control target according to an embodiment of the present invention. .

In step S10, a first draw basin [DB], which is a catch basin of a desired first drag trap (ex: 1133) among the attractors belonging to the Boolean network, may be obtained.

In step S20, a second initial state (ex: 1213), which is an undesired state, may be acquired as a state belonging to the second draw basin [UB] which is an unwanted draw basin.

In step S30, the boundary state of the first drag basin [DB] may be determined from the initial state. The boundary may mean a state according to the above definition.

In step S40, only nodes having different values among the initial state and the boundary state may be selected as control nodes to which temporary perturbation is applied.

In step S50, a temporary perturbation is applied only to the control nodes, so that the initial state can be shifted to the state of the first drag dog.

The steps S10 to S50 may be performed by a computing device. The computing device may acquire data necessary for executing the steps S10 to S50 from an external device using a wired or wireless communication means.

Hereinafter, a specific embodiment of determining the boundary state of the first drag basin [DB] from the initial state in the step S30 will be described with reference to FIG. 12.

12 is a flowchart illustrating a method of determining a boundary state of a first drag basin from a specific initial state according to an embodiment of the present invention. Here, the specific initial state is a state that is not included in the first drag basin.

In step S310, a'symmetric node' among the nodes of the Boolean network is determined.

In one embodiment, since the structural symmetric node can be determined from the structure information of the Boolean network, a logic calculation is not required for the determination. An outbound link and/or an inbound link may be connected to each node of the Boolean network. In this case, a node without an outgoing link may be regarded as a symmetric node. In addition, when another node having one outgoing link and a node connected to the one outgoing link is a symmetric node, the other node may also be regarded as a symmetric node.

For example, the outgoing link is not connected to the node G of the Boolean network 100 shown in Fig. 10A. Therefore, node G is a symmetric node. Also, the number of outgoing links from node F is one, and the next node connected to this link is node G, which is a symmetric node. Therefore, node F is also a symmetric node. After calculating the draw basin of a particular draw, dynamic symmetric nodes with symmetry may also exist.

For reference, the number of states in which the value of the symmetric node is 0 and the number of states in which the value of the symmetric node is 1 are equal to each other. That is, the average value of the states of the symmetrical nodes in a specific draw basin is 0.5. In addition, the state distributions of the nodes other than the symmetric node symmetrically coincide.

Nodes determined as symmetric nodes are nodes that do not always participate in control using temporary perturbation. That is, it is not a control target for temporary perturbation. Therefore, the symmetric node is not considered in the calculation process of the hamming distance described above. Alternatively, the symmetric node may be excluded even in the process of comparing the Hamming distance described above.

One or more of the symmetric nodes may exist in any Boolean network, or may not exist at all.

In step S320, a node whose value is always constant in all states of the desired first draw basin [DB] defined in step S10 is searched, and the searched node is determined as a'fixed node'.

For example, in the Boolean network 100 shown in FIG. 10A, node C may be a fixed node in the desired first draw basin [DB].

One or more fixed nodes may or may not exist in any draw basin.

When the value of the fixed node in the first draw basin [DB] is the same as the value of the fixed node in the initial state (ex: 1213), which is an undesired state defined in step S20, the initial In order to change from the state to the desired state of the first drag dog, the fixed node must not be temporarily perturbed.

On the contrary, when the value of the fixed node in the first draw basin [DB] is different from the value of the fixed node in the initial state (ex: 1213), the state is changed from the initial state to the desired state of the first draw. In order to change, a temporary perturbation of the fixed node must be performed.

Now, among nodes belonging to the Boolean network, the remaining nodes other than the symmetric node and the fixed node may be defined as an unfixed/asymmetric node.

In step S330. For only the non-fixed/asymmetric nodes, a hamming distance between the initial state and the respective states of the desired first draw basin [DB] may be calculated.

In step S340, a shortest distance among the calculated hamming distances may be determined, and a set of states having the shortest distance among states of the first drag basin [DB] may be determined as a boundary.

For example, in the boolean network 100 shown in FIG. 10A, non-fixed/asymmetric nodes may be node A, node B, node D, and node E.

The method for determining the boundary state according to the steps S310, S320, S330, and S340 described above is according to an embodiment of the present invention. In contrast, the above-described fixed nodes, symmetric nodes, and non-fixed/asymmetric nodes are not distinguished from each other, and each state of the initial state and the desired first draw basin [DB] for all nodes included in the Boolean network It can be understood that even if the hamming distance between them is calculated, the control node according to the embodiment of the present invention shown in FIG. 11 can be determined. However, if the preferred embodiment according to the above-described steps (S310, S320, S330, and S340) is not used, the computing power for determining the boundary state will increase.

The graph shown in FIG. 13 shows the states of a draw basin of a specific draw in a network composed of 21 nodes, and is for explaining the properties of the above-described symmetric node.

Numbers 1 to 21 on the horizontal axis of the graph shown in FIG. 13 represent 21 nodes as numbers, each row consisting of 21 values represents different states of the draw basin, and the dark part of the graph corresponds to each state. In this case, the value of each node is '1', and the bright part of the graph shows the case where the value of each node is '0' in each state.

In FIG. 13, a node with a node ID of 20 is a symmetric node, and values of the symmetric node in each state are separately displayed on the left side of the graph. In the symmetric node, the number of states whose value is '1' and the number of states whose value is '0' are the same. That is, the state average value of the symmetric node in the Boolean network is 0.5. In addition, it can be seen that the distribution of values of nodes other than the symmetric node is symmetric based on the value of the symmetric node. If the above two properties are satisfied, a symmetric node is obtained.

Due to the above two properties, the symmetrical node 20 is ignored in the unwanted initial state, and the Hamming distance to the desired attraction basin can be obtained in a state consisting of only 20 nodes. Therefore, the perturbation of the symmetric node does not affect the distance reduction. That is, the symmetric node may not participate in the control for the temporary perturbation described above.

14 shows another example of a p53 network for explaining the concept of an embodiment of the present invention.

In FIG. 14, nodes included in the first region 111 of the network structure of the p53 network 110 are all fixed nodes, all nodes included in the third region 113 are symmetric nodes, and the second region 112 The nodes included in) are all non-fixed/asymmetric nodes.

In the desired draw basin [DB] of the p53 network 110, the average value of states of the symmetric nodes is 0.5, the average value of states of PTEN and P53 among the fixed nodes is 1.0, and PTEN among the fixed nodes. And P53, the average value of the states of each of the other nodes is 0.0, and the average value of the states each of the non-fixed nodes is a value other than 0 and 1.0, and the asymmetric node has an average value other than 0.5 or 0.5. The distribution of values of nodes other than the symmetric node is not symmetric based on the value of the symmetric node.

As in the above-described method of determining a fixed node, there is no outgoing link from the Proliferation node in the third area 113. In addition, there is one link each outgoing from the P21 node and the CyclinD1 node, and the node connected to this link is a symmetric node, a Proliferation node. And there is only one link outgoing from the Bcatenin node, and the node connected to this link is the CyclinD1 node, which is a symmetric node. Accordingly, the nodes included in the third area 113 may be determined to be symmetric nodes according to the above definition.

The calculation and comparison of the hamming distance described above may be performed only for non-fixed/asymmetric nodes included in the second region 112, thereby reducing the amount of calculation.

15A is a diagram for explaining a control target according to an embodiment of the present invention.

A circle shown in FIGS. 15A to 15C represents each node, a circle with a dark background indicates a state having a value of '1', and a circle with a bright background may indicate a state having a value of '0'. . Each node can have an ID between 1 and 21, respectively. The ID for each node is displayed inside each circle.

In FIG. 15A, reference numeral 120 denotes a structure of the Boolean network 120. The boolean network 120 is composed of 21 nodes and links connecting them.

In FIG. 15A, reference numeral 1214 denotes an undesired initial state 1214 belonging to the undesired draw basin [UB], and reference numeral 1134 denotes a desired first drawer 1134 belonging to the first draw basin [DB], which is a desired draw basin. Represents.

It is necessary to first understand the following premise with respect to the Boolean network 120 shown in Fig. 15A.

First, the symmetric nodes of the Boolean network 120 are nodes with reference numbers 1 to 4. This symmetric node is determined only with the structure information of the boolean network described above. The symmetric nodes may not be considered in the process of calculating the Hamming distance between any two states and the process of selecting a control node, thereby reducing computing complexity.

Second, as a result of analyzing all the states of the desired first draw basin [DB] in which the desired first draw basin 1134 is included, the fixed nodes for the first draw basin [DB] are nodes with reference numbers 5 to 13. .

Third, non-fixed/asymmetric nodes for the desired first draw basin [DB] are nodes with reference numerals 14 to 21.

In this case, the hamming distance between the initial state 1214 and each state belonging to the first draw basin [DB] may be calculated for only the non-fixed/asymmetric nodes, that is, nodes 14 to 21.

Fourth, in the boolean network 120 shown in FIG. 15A, there are two boundary states of the first draw basin [DB] from the initial state 1214, and the first boundary ( 1127) and the second boundary 1128.

A method of determining a control node according to an embodiment of the present invention will now be described with reference to FIGS. 15B and 15C together.

15B is a list of states of fixed nodes 5 to 13 and non-fixed/asymmetric nodes 14 to 21 in the initial state 1214 and the first boundary 1127.

In the initial state (1214), the values of the fixed nodes (5, 7, 9, 12, 13) and non-fixed/asymmetric nodes (15, 17, 21) are '0', and the fixed nodes (6, 8, 10, 11) ) And the non-fixed/asymmetric nodes 14, 16, 18, 19, 20 are '1'.

In the first boundary 1127, the values of the fixed nodes (5, 6, 7, 9, 10, 12, 13) and the non-fixed/asymmetric nodes (15, 17, 18) are '0', and the fixed node (8, 11) and the non-fixed/asymmetric nodes 14, 16, 19, 20, 21 have a value of '1'.

That is, when the initial state 1214 and the state of the first boundary 1127 are compared with each other, only the values of the fixed nodes 6 and 10 and the non-fixed/asymmetric nodes 18 and 21 are different from each other. Therefore, when the boolean network 120 is in the initial state 1214, if only the values of the fixed nodes 6 and 10 and the non-fixed/asymmetric nodes 18 and 21 are temporarily perturbed, the boolean network 120 The state changes to the first boundary state 1127, and in the end, the state may change to the first drawer 1134, which is a drawer of the first draw basin [DB] to which the first boundary state 1127 belongs.

15C is a list of states of fixed nodes 5 to 13 and non-fixed/asymmetric nodes 14 to 21 in the initial state 1214 and the second boundary 1128.

As described in connection with FIG. 15B, when comparing the states of the initial state 1214 and the second boundary 1128 in FIG. 15C, only the values of the fixed nodes 6 and 10 and the non-fixed/asymmetric nodes 14 and 21 These are different from each other. Therefore, when the boolean network 120 is in the initial state 1214, if only the values of the fixed nodes 6 and 10 and the non-fixed/asymmetric nodes 14 and 21 are temporarily perturbed, the boolean network 120 The state changes to the second boundary state 1128, and eventually the state may change to the first drawer 1134, which is a drawer of the first drawer basin [DB] to which the second boundary state 1128 belongs.

The example described with reference to FIGS. 15A to 15C shows a case in which a total of two boundary states are present. In this example, only the first set of nodes consisting of four nodes 6, 10, 18, 21 is perturbed as shown in FIG. 15B, or four nodes 6, 10, 14, 21 as shown in FIG. 15C. By perturbing only the configured second set of nodes, the Boolean network 120 may be changed to a desired state of the first drawer 1134.

In contrast, even if five or more nodes are perturbed, the initial state 1214 may be changed to an arbitrary state belonging to the first drag basin [DB]. However, according to the exemplary embodiment of the present invention described above, only the smallest number of nodes can be perturbed to change to a desired state of the first drawer 1134. Each node can mean a different protein, and because different drugs may need to be administered together to perturb the state of different proteins together, a good technical effect can be obtained by minimizing the number of nodes to perturb. .

III. Computing devices and devices

16 is a diagram illustrating a computing device and devices communicating with the computing device provided according to an embodiment of the present invention.

The computing device 910 includes a communication interface 930, a processing unit 910, and a storage unit 920 that communicate with the external device 940 by wire or communicate with the external devices 960 and 970 by wire or wirelessly. Can include.

The external device 940 may be, for example, a portable recording device such as USB or an external hard disk. The external device 960 may be a database device containing data. The external device 970 may be a device in which downloadable command codes are recorded.

The network 950 may be one of various networks such as a LAN, MAN, LTE, wireless communication, and a network for short-range wireless communication.

The processing unit 910 may be various processing devices such as a CPU, MCU, FPGA, and CUDA processor.

The storage unit 920 may be, for example, a volatile memory (ex: RAM) and/or a non-volatile storage (ex: SDD, HDD) included in the computing device 910.

At this time, the processing unit 910 includes information on the structure of the Boolean network, information on the initial state of the Boolean network, and information about the Boolean network from the external device 940 or 960 through the communication interface 930. It is to acquire information on the first drag catcher belonging to the desired first drag catchment basin that does not include the initial state among the catchers, and determines the boundary state of the first drag catch basin from the initial state, and the boolean Among the nodes of the Lean network, nodes having different states of the boundary state and the initial state may be determined as control nodes. In this case, the boundary state may be a state having a minimum hamming distance among hamming distances between the initial state and respective states belonging to the first claw basin among states belonging to the first claw basin.

The storage unit 920 or the external device 970 connected to the computing device 900 through the network 950 may be a computer-readable non-transitory storage device in which a program is recorded. In this case, the program may be composed of sets of instructions that cause the processing unit 910 of the computing device 900 to execute the above-described functions and steps.

Using the above-described embodiments of the present invention, those belonging to the technical field of the present invention will be able to easily implement various changes and modifications within the scope not departing from the essential characteristics of the present invention. The content of each claim in the claims may be combined with other claims that do not have a citation relationship within the range that can be understood through the present specification.

Claims (15)

Determining, from an initial state of the Boolean network, a boundary state of a desired first draw basin in which the initial state is not included; And
Determining, as a control node, nodes having different states when comparing the boundary state and the initial state among the nodes of the boolean network;
Including,
The boundary state is a state having a minimum Hamming distance among hamming distances between the initial state and respective states belonging to the first claw basin among states belonging to the first claw basin,
How to determine the control node of the Boolean network. The method of claim 1, further comprising perturbing the control node among nodes of the boolean network in the initial state. The method of claim 2, wherein the perturbation of the control node is performed only temporarily. The method of claim 1,
The step of determining the boundary state,
A fixed node determining step of determining a fixed node defined as a node whose value is always constant in all states of the first draw basin among the nodes of the boolean network;
A hamming distance calculation step of calculating a hamming distance between the initial state and each state included in the first draw basin; And
Determining a state having a minimum Hamming distance from the initial state among states belonging to the first draw basin as a boundary state;
Including,
The hamming distance is a hamming distance between the initial state and each state included in the first claw basin, calculated for only nodes other than the fixed node among the nodes of the Boolean network,
How to determine the control node of the Boolean network. The method of claim 4,
The hamming distance calculation step further includes calculating a partial hamming distance between the initial state and each state included in the first draw basin,
The partial hamming distance is a hamming distance calculated for only non-fixed nodes and asymmetric nodes, which are nodes excluding the symmetric node and the fixed node,
The determining of the boundary state may include a state having a minimum distance among the partial hamming distances between the initial state and each state belonging to the first draw basin among states belonging to the first draw basin. Including the step of determining to be in the boundary state,
How to determine the control node of the Boolean network. The method of claim 4,
Further comprising the step of determining a symmetric node among the nodes of the Boolean network,
The symmetric node includes a structural symmetric node defined as a node that does not have an outgoing link in the structure of the Boolean network,
The hamming distance is a hamming distance between the initial state and each state included in the first drag basin, calculated for only nodes other than the fixed node and the symmetric node among the nodes of the Boolean network,
How to determine the control node of the Boolean network. The Boolean network according to claim 6, wherein the symmetric node has only one outgoing link in the structure of the Boolean network, and a node connected to the outgoing link further comprises another structural symmetric node, which is the structural symmetric node. How to determine the control node of The dynamic symmetry of claim 7, wherein the symmetric node has an average value of 0.5 when the values of the states of the Boolean network are averaged for each node, and the remaining states are defined as a symmetric node based on the node. A method for determining a control node of a Boolean network, further comprising a node. The method of claim 4,
Further comprising the step of determining a symmetric node among the nodes of the Boolean network,
The symmetric node includes a dynamic symmetric node defined as a node whose average value is 0.5 when the values of the states of the Boolean network are averaged for each node, and the remaining states are symmetrical based on the node,
The hamming distance is a hamming distance between the initial state and each state included in the first drag basin, calculated for only nodes other than the fixed node and the symmetric node among the nodes of the Boolean network,
How to determine the control node of the Boolean network. The method of claim 1, wherein the boolean network is a model of a biomolecule signaling network, and each node of the boolean network corresponds to each molecule of the biomolecule signaling network. . The method of claim 1,
The method of determining all the states belonging to the first claw basin,
Acquiring information on a first drawer belonging to the first drawbridge basin;
Initializing the reference state of the boolean network to the first draw; And
① A state backtracking step of calculating the immediate previous state of the Boolean network based on the first update rule, which is the update rule of the state of the Boolean network, and ② the reference state of the Boolean network. The reference state is The state backtracking step is defined as the state of the Boolean network of, and the immediately preceding state is defined as the state of the Boolean network at a point immediately preceding the point of time immediately before the reference point of time.
Including,
For each of the calculated immediately preceding states, by repeating the state backtracking step after updating the reference state to the calculated immediately preceding state, determining all states of the first draw basin including the first draw catch. Characterized by,
How to determine the control node of the Boolean network. The method of claim 11,
For those determined to be the terminal state among the calculated immediately preceding states, the qualification as the state of the first network at the reference point in time is not granted, and the state backtracking step is not repeated,
The terminal state is a state in which a previous state does not exist on a state transition path including the terminal state,
How to determine the control node of the Boolean network. The method of claim 11,
In the boolean network, a symmetric node has been removed from the first boolean network,
In the first drawer of the boolean network, a value of the removed symmetric node is removed from a specific drawer of the first boolean network,
How to determine the control node of the Boolean network. A computing device including a communication interface and a processing unit that communicates with an external device by wire or wirelessly,
The processing unit,
From the external device through the communication interface, information about the structure of the Boolean network, information about the initial state of the Boolean network, and a desired first draw basin in which the initial state is not included among the drawers of the Boolean network. It is supposed to acquire information about the first draw that it belongs to,
It is configured to determine the boundary state of the first draw basin from the initial state, and
When comparing the boundary state and the initial state among the nodes of the boolean network, nodes having different states are determined as control nodes,
The boundary state is a state having a minimum Hamming distance among hamming distances between the initial state and respective states belonging to the first claw basin among states belonging to the first claw basin,
Computing device. The processing unit of the computing device including a communication interface and a processing unit for communicating with an external device by wire or wirelessly,
From the external device through the communication interface, information about the structure of the Boolean network, information about the initial state of the Boolean network, and a desired first draw basin in which the initial state is not included among the drawers of the Boolean network. Acquiring information on the belonging first draw;
Determining a boundary state of the first drag basin from the initial state; And
Determining, as a control node, nodes having different states when comparing the boundary state and the initial state among the nodes of the boolean network
As a computer-readable non-transitory storage device in which a program for executing a program is recorded,
The boundary state is a state having a minimum Hamming distance among hamming distances between the initial state and respective states belonging to the first claw basin among states belonging to the first claw basin,
Computer-readable non-transitory storage.

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