KR102452630B1 - An optimized method of searching a boundary state of a Boolean network with minimal complexity of distance calculation using structural information and basin information of the Boolean network - Google Patents

Abstract

A fixed node determination step of determining, among nodes of the Boolean network, a fixed node defined as a node whose value is always constant in all states of the first attracting basin that does not include a predetermined initial state of the Boolean network , a Hamming distance calculation step of calculating the Hamming distance between the initial state and each state included in the first attracting basin, and a state having a minimum Hamming distance from the initial state among the states belonging to the first attracting basin boundary state and determining that the Hamming distance is between the initial state and each state included in the first attraction basin, which is calculated for only nodes except for the fixed node among the nodes of the Boolean network. Discloses a boundary state determination method, characterized in that the Hamming distance.

Description

An optimized method of searching a boundary state of a Boolean network with minimal complexity of distance calculation using structural information and basin information of the Boolean network}

The present invention relates to a technique for quickly finding a state having a minimum Hamming distance from an initial state of the Boolean network that is not included in the attracting basin among states included in a specific attracting basin of a Boolean network, Computing technology It relates to information processing technology using

In order to change the state of a cell in an undesirable 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. In this case, if the same effect can be obtained by administering fewer types of drugs, it may be more preferable in terms of cost and minimizing side effects of drugs.

Changes in the phenotype of cells can be modeled and analyzed by biomolecular signaling networks. In addition, the biomolecule signal processing network may be modeled as a Boolean network. The Boolean network may include nodes and links connecting the nodes, and each node 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 an attractor landscape used therewith. By 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 attraction topography.

In the prior art for finding the basin of attraction of a specific attractor of a 'Boolean network', in all possible states of the system, the state transition path to the particular attractor is calculated by applying a given update rule and converges to the particular attractor. By using the process of finding the state transition path, a state transition diagram of the entire specific attracting basin is obtained.

The inventor of the present invention has developed a technique for determining a target control node to be controlled among nodes included in the Boolean network in order to change the value of a specific output node of the Boolean network to a desired value. The method for determining the target control node of the Boolean network includes the steps of: ① determining the boundary state of a desired first attracting basin that does not include the initial state from a given initial state of the Boolean network; and ② nodes of the Boolean network. and finding nodes having different states when comparing the determined boundary state with the given initial state, and determining the found nodes as target control nodes.

In this case, the boundary state may be defined as a state having a Hamming distance closest to the initial state among states belonging to the first attraction basin. That is, the boundary state may be determined according to the value of the initial state. For example, the value of the first boundary state when the first initial state is given may be different from the value of the second boundary state when the second initial state different from the first initial state is given. However, in order to determine the boundary state for a given initial state, since a calculation process according to a predetermined method must be performed for all states belonging to the first attractor basin, if the size of the first attractor basin increases, many computing There is a problem that power may be required.

The above description is based on the contents known or studied by the inventor of the present invention in order to help the understanding of the present invention. Therefore, it should not be considered that all of the above contents were disclosed to an unspecified person prior to the application of the patent of the present invention.

In the present invention, among the states belonging to the first attraction basin of the Boolean network, it is intended to provide a technique for rapidly calculating the boundary state defined as the state having the minimum Hamming distance from the given initial state of the Boolean network.

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. The 'state' of a Boolean network can be expressed as an ordered pair of values of all nodes. According to this, when the total number of nodes in the Boolean network is N, the number of possible states is 2 ^N. A Boolean network may have a specific state at a specific moment, and as time passes, the state of the Boolean network may change or remain the same.

- Attractor: A set of states that repeat over time among states of a Boolean network can be referred to as an 'attractor'. The attraction may correspond to a 'phenotype', which means a condition such as cancer or apoptosis in the case of a living system.

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

- Basin of Attraction: A set consisting of all states included in all state transition paths toward a specific attraction can be referred to as a 'basin of attraction'. All the states included in the specific attracting basin may converge to the attracting state of the specific attracting 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 point 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 having different values between 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 whose values are different from each other when comparing the first and second states 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 three. 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 attracting basin [DB], the state that is the shortest Hamming distance from the unwanted second state [US] included in the unwanted second attracting basin [UB] is the 'boundary state' ', or 'the boundary state of the desired first attractor basin [DB] from the second undesired state [US]'. ] may exist one or more boundary states. The set of boundary states may be referred to as a 'boundary' or a 'boundary of the first desired attraction basin [DB] from the undesired second state [US]'.

'D' indicated in [] as described herein may mean 'desired', 'U' may mean 'undesired', and 'B' may mean 'attractive watershed' (basin)' may mean 'S' may mean 'state'.

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

- Temporary perturbation: Temporarily changing the value of a node can be referred to as 'temporary perturbation'. If the perturbation is stopped immediately after temporarily changing the values of one or more nodes, the state change of the Boolean network is made according to its inherent dynamics. In an 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 in a way that forcibly and continuously fixes the value. According to this comparative example, since the value of a specific node is forcibly fixed, the Boolean network may not behave according to its own dynamics.

-Initial state: In the present invention, as a state in which provision of temporary perturbation is required or a temporary perturbation must be applied, for example, an unwanted second state [US] belonging to the unwanted second attraction basin [UB] is ' It can also be referred to as 'initial state'. Accordingly, the boundary state may be referred to as 'the boundary state of the desired first attraction basin [DB] from the initial state'.

- Symmetric nodes: Symmetric nodes can be classified into two types. First, a 'structural symmetric node' is a symmetric node determined only from the network structure, and is always a symmetric node in all the attraction basins. Second, the 'dynamically symmetric node' is an additional symmetric node that appears according to the dynamic characteristics of each attraction in addition to the structural symmetric node. Structural symmetric nodes can be known without calculating the basin of attraction, but the dynamic symmetric node calculates a specific basin of attraction. You can only find out after doing it.

A node with no outgoing links in the network structure can be considered to be a 'structurally symmetric node'. In addition, when there is 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 concrete meaning of 'symmetry', let N=3, there are nodes A, B, and C, and node A is a structurally symmetric node found from the network structure. If there is a state (A, B, C)=(0, b, c) in a particular catchment, then the state (A, B, C)=(1, b, c) must also exist in that catchment. Since node A causes this symmetry, it can be referred to as a symmetric node.

Alternatively, although it is not a structurally symmetric node, there may exist a node satisfying the symmetry described in the above example (N=3, nodes A, B, and C) when the basin of attraction of a specific attraction is calculated. Since it is a symmetric node that can be known after calculating the catchment basin, it can be referred to as a 'dynamically symmetric node'.

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

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

According to one aspect of the present invention, among the nodes of the Boolean network, in all states of the first attracting basin that does not include the predetermined initial state of the Boolean network, a fixed value is defined as a node whose value is always constant. a fixed node determining step of determining a node; Hamming distance calculation step of calculating a Hamming distance between the initial state and each state included in the first attracting basin; and determining a state having a minimum Hamming distance from the initial state among states belonging to the first attraction basin as a boundary state; The Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, calculated for only nodes excluding the fixed node among the nodes of the Boolean network.

In this case, the method for determining the boundary state further includes determining a symmetric node among the nodes of the Boolean network, wherein the symmetric node is structurally symmetric defined as a node having no outgoing link in the structure of the Boolean network. It includes a node, and the Hamming distance is between the initial state and each state included in the first attraction basin, which is calculated by targeting only nodes excluding the fixed node and the symmetric node among the nodes of the Boolean network. It could be a hamming distance.

In this case, the symmetric node may further include another structurally symmetric node having only one outgoing link from the structure of the Boolean network, and the node connected to the outgoing link being the structurally symmetrical node.

In this case, the symmetric node, when the values of the states of the Boolean network are averaged for each node, the average value is 0.5, and further includes a dynamic symmetric node defined as a node in which the remaining states are symmetric with respect to the node. can do.

In this case, the method for determining the boundary state may further include determining a symmetric node among nodes of the Boolean network. And the symmetric node, when the values of the states of the Boolean network are averaged for each node, the average value is 0.5, and includes a dynamically symmetric node defined as a node in which the remaining states are symmetric with respect to the node, The Hamming distance may be a Hamming distance between the initial state and each state included in the first attraction basin, calculated by targeting only nodes excluding the fixed node and the symmetric node among the nodes of the Boolean network. .

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.

At this time, the method for determining all the states belonging to the first attractor basin includes the steps of: obtaining information about the first attractor belonging to the first attractor basin; initializing the reference state of the boolean network to the first decoupling; and ① a first update rule that is an update rule of the state of the Boolean network, and ② a state backtracking step of calculating the immediately preceding state of the Boolean network based on a reference state of the Boolean network, wherein the reference state is a reference point It is defined as the state of the Boolean network in , and the immediately preceding state is defined as the state of the Boolean network at a time immediately preceding the reference time, and may include the step of tracing back the state. And 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 attractor basin including the first attractor can be determined. have.

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

In this case, the Boolean network has a symmetric node removed from the first Boolean network, and the first attraction of the Boolean network is that the value of the removed symmetric node is removed from a specific attraction of the first Boolean network. can

In this case, the method for determining the boundary state may further include determining, as a control node, nodes having different states when the boundary state and the initial state are compared with each other among the nodes of the Boolean network.

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. At this time, the processing unit obtains information about the Boolean network from the external device through the communication interface, and among the nodes of the Boolean network, a first attraction basin that does not include a given initial state of the Boolean network. Determine a fixed node, which is defined as a node whose value is always constant in all states of , calculate the Hamming distance between the initial state and each state included in the first attractor basin, and in the first attractor basin Among the states to which it belongs, a state having a minimum Hamming distance from the initial state is determined to be a boundary state. In addition, the Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, calculated for only nodes excluding the fixed node among the nodes of the Boolean network.

According to another aspect of the present invention, the processing unit of a computing device including a communication interface and a processing unit for communicating with an external device by wire or wirelessly acquires information about a Boolean network from the external device through the communication interface to do; A fixed node determination step of determining, among the nodes of the Boolean network, a fixed node defined as a node whose value is always constant in all states of the first attraction not including the given initial state of the Boolean network ; calculating a Hamming distance between the initial state and each state included in the first attraction basin; and determining that a state having a minimum Hamming distance from the initial state among states belonging to the first attraction basin is a boundary state; a computer-readable non-transitory storage device in which a program to execute is recorded is provided can be In this case, the Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, calculated for only the nodes excluding the fixed node among the nodes of the Boolean network.

According to another aspect of the present invention, using the above-described boundary state determination method, from an initial state of a Boolean network, determining a boundary state of a desired first attraction basin that does not include the initial state; and determining, among nodes of the Boolean network, nodes having different states as control nodes when the boundary state and the initial state are compared with each other. can

According to the present invention, among the states belonging to the first attracting basin of the Boolean network, the state having the minimum Hamming distance among the Hamming distances between the initial state of the Boolean network and each state belonging to the first attracting basin We can provide a technique to quickly compute the boundary state defined as

In addition, according to the present invention, in order to change the value of a specific output node of the Boolean network to a desired value, an algorithm for determining a target node to be controlled among nodes included in the Boolean network can be executed at a faster speed. technology can be provided.

1 is a first state transition path and a first state transition path showing a series of states in the process of changing with time from a first terminal state to a specific attraction in a specific attraction basin of a given first Boolean network. This shows the concept of the first inverse-state transition path, which is a path going 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 .
4 is a representation of the node classified as a crystalline node in FIG. 3 as a rectangle.
5 shows the values of each node at the immediately preceding time point among the values of each node of the first subnetwork on the left side, and the values of each node at the reference time point immediately after the immediately preceding time point are arranged on the right side at the reference time point. It is a schematic diagram of which node is affected by the value of each node at the previous point in time.
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 attractor basin to which a specific attractor 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 attraction, an attraction, an initial state, and a state transition path used in an embodiment of the present invention.
FIG. 10 is a further refinement 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 that is 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 attraction basin from a specific initial state according to an embodiment of the present invention.
The graph shown in FIG. 13 shows the states of the catchment basin of a specific attraction in a network consisting of 21 nodes, and is for explaining the properties of the aforementioned symmetric node.
14 shows an example of another 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 shows the states of fixed nodes and non-fixed/asymmetric nodes in the initial state and the first boundary.
15C shows the states of fixed nodes and non-fixed/asymmetric nodes in the initial state and the second boundary.
16 is a flowchart of a method for determining a boundary state provided according to an embodiment of the present invention.
17 is a diagram illustrating a computing device provided according to an embodiment of the present invention and devices communicating therewith.

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 herein and may be implemented in various other forms. The terminology used in this specification is intended to help the understanding of the embodiment, and is not intended to limit the scope of the present invention. Also, singular forms used hereinafter include plural forms unless the phrases clearly indicate the opposite.

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

1 is a first state transition path ( 3101) and the first inverse-state transition path R3101, which is a path that traverses the first state transition path in time.

A closed curve with a dotted line in FIG. 1 shows the terminal states among the states of the specific attraction basin.

In an embodiment of the present invention, on the premise that the value of the specific attraction 1131 can be known, by calculating all inverse-state transition paths starting from the specific attraction 1131 by going backwards in time from the specific attraction 1131 . It is possible to determine the values of all states of the particular attracting 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 help the understanding of the present invention.

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

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

In the first Boolean network illustrated in FIG. 2 , the structurally symmetric node is X ₅ .

In step S13 according to an embodiment of the present invention, a first subnetwork obtainable 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 that is an update rule of the state of the first subnetwork may be determined based on the information on the structure of the first subnetwork.

For example, the first update rule may be given as the following equations 1 to 4 without a structurally symmetric node X ₅ . Equations 1 to 4 each have two sides. The left side shows the state of each node at the reference time point (= future time point), and the right side shows the state of each node at the point immediately before the reference point (= past time point).

Here, the state of the sub-network at the immediately preceding time is changed to the state of the sub-network at the reference time without passing through other states. That is, the immediately preceding time point is a time point immediately before the reference time 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 the information on the structure of the first subnetwork, the state at the immediately preceding time point (=past time point) of the arbitrary first node is the It is determined whether or not it is uniquely determined by the state at the reference point (= future time point) of the first subnetwork, and if it is uniquely determined, the first node is classified as a deterministic 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 of the node X ₁ and the node X ₂ at the immediately preceding time point is uniquely determined by the state at the immediately subsequent reference time point. Accordingly, the nodes X ₁ and X ₂ are classified as the deterministic nodes.

In Equations 1 to 4, it can be seen that the state of the node X ₃ and the node X ₄ at the immediately preceding time point is not uniquely determined by the state at the reference time point. Accordingly, the nodes X ₃ and X ₄ are classified as the non-deterministic nodes.

4 is a representation of the node classified as a crystalline node in FIG. 3 as a rectangle.

A node having a plurality of outbound links among the nodes classified as the deterministic node in step S22 according to an embodiment of the present invention may be classified as a determining node.

Referring to the structure of the first subnetwork shown in FIG. 3 , _two outbound links from node X1 among the deterministic nodes are plural, and _one outbound link from node X2 among deterministic nodes is one. As a dog, it is not a plural dog. Accordingly, in the case of the first subnetwork shown in FIG. 3, the discriminating node is the node _X1 .

5 shows the values of each node at the immediately preceding time point among the values of each node of the first subnetwork on the left side, and the values of each node at the reference time point immediately after the immediately preceding time point are arranged on the right side at the reference time point. It is a schematic diagram of which node is affected by the value of each node at the previous point in time. The structure of Fig. 5 can be easily understood from the link of Fig. 3 or Fig. 4 .

When a subnetwork according to another example is given, there may be no discrimination node or there may be a plurality of determination nodes.

The first update rule may be presented again by Equations 5 to 8 below. Equations 5 to 8 below may also be considered 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 update rule may be presented again by Equations 9 to 12 below. Equations 9 to 12 below may also be considered 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, the It can be checked whether the discriminant node is included in the first side representing the past state (=immediate state) that is the state of the subnetwork.

For example, in Equations 9 to 12, the first side representing the past state at the immediately preceding time point 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 including the discrimination node on the first side may be selected.

For example, in the example of step S22, the discriminant node is the node X ₁ , and in Equations 9 to 12, the equations including the 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 time point immediately following the immediately preceding time point is the above-described terminal state can decide

For example, referring to Equations 10 and 12, in the selected equation, in order for a value of X ₁ that is a valid past state to exist, the relation X ₁ =X ₂ ^* =X ₁ =￢X ₄ ^* must be established. That is, only when the relation X ₂ ^* =￢X ₄ ^* is established, X ₁ , which is the immediately preceding value of the given X ₁ ^* , can exist effectively.

Conversely, if the relationship X ₂ ^* =￢X ₄ ^* does not hold, that is, if the relationship X ₂ ^* =X ₄ ^* holds, X ₁ , which is the immediately preceding value of X ₁ ^* , does not exist effectively. can That is, if a state in which a relationship of X ₂ ^* =X ₄ ^* is established among the possible states of the first subnetwork is given, it can be seen that there is no state of another value occurring before the given state. And by the above definition, the given state may be regarded as a terminal state.

At this time, the An expression defined by X ₂ ^* =X ₄ ^* may be defined as the above-described discriminant. Equation 13 below is a discriminant for determining whether a specific state that can be obtained from the first subnetwork 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 ] = [discriminate] X ₂ ^* =X ₄ ^*

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

For example, the values of each node (X ₁ to X ₅ ) of the first Boolean network in the specific attraction 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 below.

The 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

The 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, it is possible to obtain a first attraction of a first subnetwork that is a subnetwork of the first Boolean network.

For example, the value of each node of the first subnetwork in the first attraction 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 subnetwork at the first time point may be referred to as a 'reference time state', a 'first time point state', or a 'first layer state'. If the first attraction is a point attractor (point attractor), the 'state of the reference point' in the first attractor basin, which is the basin of the first attractor, may exist. In comparison with this, when the first attractor is a cyclic attractor, the 'state of the reference point' in the first attractor basin, which is the basin of the first attractor, may exist. Tables 3 and 4 show a case in which the first attractor is a cyclic attractor.

1st 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 the step (S41) according to an embodiment of the present invention, using ① the value of the first attraction of the first subnetwork and ② the first update rule, at the time immediately before the reference point (= second time point) It is possible to calculate any one of the states of the first subnetwork of .

In the present specification, the state of the first sub-network at the second time point immediately before the reference time point may be referred to as 'the state of the immediate time point', 'the state of the second time point', or 'the state of the second layer'. . The state of the immediately preceding time point may be absent, one, or plural.

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

The first state at the time immediately preceding (example) X ₁ X ₂ X ₃ X ₄ One 0 0 One

It can be seen that the first state at the immediately preceding time point presented in Table 5 is the same as the second state (= cyclic attraction) at the reference time point. Therefore, it can be understood that, according to the nature of the cyclic attraction, the state at the third time point that occurs earlier than the immediately preceding time point becomes the same as the first 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 in Table 4, Another one of the states, 'the second state at the immediate time point', is calculated, and may be presented as shown in Table 6.

The second state at the time immediately preceding (example) X ₁ X ₂ X ₃ X ₄ 0 One One 0

It can be seen that the second state at the immediately preceding time point presented in Table 6 is the same as the first state (= cyclic attraction) at the reference time point. Accordingly, it can be understood that the state at the third time point, which occurs 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 in Table 4, Another one of the states, 'the third state at the immediate time point', is calculated, and may be presented as shown in Table 7.

3rd state at the time immediately preceding (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 in Table 4, If another one of the states, 'the fourth state at the immediate time point', is calculated, it can be presented as shown in Table 8.

3rd state at the time immediately preceding (example) X ₁ x ₂ X ₃ X ₄ 0 One 0 0

Summarizing the states presented in Tables 3 to 8 above, {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 as the state of the immediately preceding time point (the second layer or the second time 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 It can be seen that there are 4 of ₄ } = {0,1,0,0}.

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

In this case, whether the terminal state exists among the newly calculated four immediately preceding point-in-time states can be checked using the discriminant. After this check operation, computing power is reduced because there is no need to go through the process of obtaining the previous state issued prior to the immediately preceding state for the state of the immediately preceding time point confirmed to be the terminal state. That is, the following step S51 may be executed.

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

For example, the discriminant derived for the first subnetwork is Equation 13, and states {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}, {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1 ,1} only satisfies the above discriminant. Accordingly, it can be determined that only the third state of the immediately preceding time point is the terminal state.

In step (S61) according to an embodiment of the present invention, among the states of the immediately preceding time point, ① not a terminal state and ② qualification as a new reference point state to a state determined not to be an attraction (= first attraction) and the state of the immediately preceding time may be determined for each of the states of the new reference time point.

For example, {X ₁ , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1}, {X ₁ found to be an attraction (= first attraction) among the four states of the immediately preceding time point , X ₂ , X ₃ , X ₄ } = {1, 0, 0, 1} cannot be qualified as the state of the new reference point. In addition, {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,1,1}, which is determined to be a terminal state, among the states of the four immediately preceding time points, is qualified as the state of the new reference time point. cannot be granted

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

Accordingly, by taking {X ₁ , X ₂ , X ₃ , X ₄ } = {0,1,0,0} as the state of the reference time, the state of the immediately preceding time may be generated according to the update rule.

By repeating the above-mentioned steps, if a state that can be qualified as the state of the new reference point is no longer found, all of the first attractors included in the first attractor basin to which the first attractor of the first subnetwork belongs. The status can be considered determined.

In step S71 according to an embodiment of the present invention, by adding the value of the removed symmetric node to all state values of the determined first attraction basin, the specific attraction of the first Boolean network belongs to. It is possible to determine all the states of a particular catchment basin.

In this case, as the value of the symmetric node, all values that the symmetric node may have may be added. For example, when the removed symmetric node is one, the number of all states of the specific attracting basin of the first Boolean network may be twice the number of all states of the first attracting basin of the first subnetwork.

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 given first Boolean network may be obtained in step S11.

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

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

In step S14, a first update rule that is an update rule of the state of the first subnetwork may be determined based on the information on the structure of the first subnetwork.

In step S21, from the first update rule or from information about the structure of the first subnetwork, the state at the immediately preceding time point (=past time point) of any first node is the reference point of the first subnetwork ( = future time), it is determined whether or not it is uniquely determined, and when it is uniquely determined, the first node is classified as a deterministic node. can be classified as

A node having a plurality of outbound links among the nodes classified as the deterministic node in step S22 may be classified as a determining node.

In step S23, the state of the sub-network among both sides of each of the equations (Equations 1 to 4, or 5 to 8, or Equations 9 to 12) included in the first update rule, the past state ( = It can be checked whether the discriminant node is included in the first side representing the previous state).

In step S24, from among the equations included in the first update rule, equations including the discriminant node 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 time point immediately following the immediately preceding time point is the above-described terminal state may be determined.

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

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

In step S32, it is possible to obtain a first attraction of a first subnetwork that is a subnetwork of the first Boolean network.

In step S41, using ① the value of the first attraction of the first subnetwork and ② the first update rule, the state of the first subnetwork at the time immediately preceding the reference point (= second time point) Any one of them can be calculated.

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

In step S61, among the states of the immediately preceding time point, ① not a terminal state and ② a state determined not to be an attraction (= first attraction) is qualified as a state of a new reference point, and the new reference point of time is For each of the states, the state of the immediately preceding time may be determined.

In step S71, by adding the value of the removed symmetric node to all the determined state values of the first attractor basin, all states of the particular attractor basin to which the particular attractor of the first Boolean network belongs are determined. can

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

As described above, according to an embodiment of the present invention, even if the topography of the attraction of the Boolean network is not completely known, all states of a specific attractor basin to which a desired specific attractor of the Boolean network belongs can be quickly determined. Hereinafter, application cases that can be performed using all the conditions of the specific attracting basin determined in this way are presented.

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

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

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

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

State 1211 is a second undesired state [US] 1211 belonging to the second undesired attracting basin [UB]. That is, the state 1211 is a first initial state 1211 that is an initial state that needs to provide temporary perturbation or needs to apply temporary perturbation.

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

In particular, state 1111 represents a terminal state 1111 in the time domain for which a previous state does not exist, state 1121 represents a boundary state from an undesired state 1211, and state 1131 represents a desired state. A desired first attractor 1131 that is an attractor of the first attractor basin [DB] is indicated.

Reference number 2101 denotes a set of states having the same Hamming distance HD1 as the terminal state 1111 from the first initial state 1211, and reference number 2102 denotes the same as the first pulley 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 a boundary state 1211 from the first initial state 1211 . At this time, the relationship mHD < HD1 < HD2 is established.

In FIG. 8, on the state transition path 3101, the boundary state 1121 of the first attracting basin [DB] from the first initial state 1211 is assumed to exist, but the first attracting basin [DB] is not shown. In another state transition path, the boundary state of the first attraction 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 attraction, an attraction, 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 attraction basin [DB], respectively.

Reference numeral 1212 denotes a second initial state 1212 that is a state included in the unwanted second attracting basin [UB] and is an initial state in which provision of a temporary perturbation is required or a temporary perturbation must 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 of 4 from the second initial state 1212, and reference number 2204 denotes a fourth set of states having a Hamming distance of 5 from the second initial state 1212, And 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 , the 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 chute 1132 belongs to the fourth set. And the boundary states 1123 and 1125 all belong to the sixth set [m].

Among all the circles shown in FIG. 9, all other circles except for the second initial state 1212 are included in the desired first attracting basin [DB].

FIG. 10 is a further refinement 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 FIG. 10A , 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 seven nodes and links connecting these nodes.

FIG. 10(b) is a diagram illustrating a value of one state of the Boolean network shown in FIG. 10(a). A set of seven nodes attached to each other in FIGS. 10(b), 10(c), and 10(d) represents one state.

In (b) of FIG. 10 , the node of the thin outline 101 represents the first binary value '1' among binary values 0 and 1 that each node of the Boolean network can have, and the node of the thick outline 102 is It 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 (c) of FIG. 10 , the state 1133 indicates a desired first caisson 1133 . A plurality of state transition paths toward the desired first attraction 1133 exist, and are indicated 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 attracting basin [DB], which is the desired first attracting basin 1133, can be known, but in FIG. Shows only the desired first attraction (1133) and the terminal state (1116) of some terminal states.

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

In the example shown in (d) of Figure 10, the hamming distance (HD) between the second initial state 1213 and the desired first attraction 1133 is 4, and the second initial state 1213 and the boundary state ( 1126), the minimum Hamming distance (mHD) between them is assumed to be 1. In the example shown in FIG. 10D , only the value of the node C is different from the second initial state 1213 and the boundary state 1126 . Therefore, if only the value of the node C in the second initial state 1213 is temporarily perturbed, that is, temporarily changed, the state of the given Boolean network 100 is the state belonging to the desired attraction basin [DB], the boundary state ( 1126) is changed. As a result, the state of the given Boolean network 100 eventually arrives at the desired state of the attraction 1133 along the state transition path to which the boundary state 1126 belongs.

According to the concept shown in FIG. 10 , a method for determining a control node according to an embodiment of the present invention can be described as 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 that is a control target according to an embodiment of the present invention. .

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

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

In step (S30), it is possible to determine the boundary state of the first attracting basin [DB] 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 should be applied.

In step S50, by applying a temporary perturbation only to the control nodes, it is possible to transition the initial state to the state of the first attraction.

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

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

12 is a flowchart illustrating a method of determining a boundary state of a first attraction 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 attraction basin.

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

In one embodiment, since the structurally symmetric node can be determined from the structural information of the Boolean network, there is no need to perform a logic calculation for the determination. Each node of the Boolean network may be connected to an outbound link and/or an inbound link. In this case, a node having no 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, an 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 links outgoing 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 area of attraction of a specific attraction, there may also be dynamic symmetric nodes with symmetry.

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 among states belonging to a certain attraction basin are the same. That is, the average value of the states of a symmetric node in a specific attraction basin is 0.5. In addition, the state distribution of the remaining nodes except for the symmetric node is symmetrically identical.

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

In any boolean network, one or more or none of the symmetric nodes may exist.

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

For example, in the Boolean network 100 shown in FIG.

There may be one or more fixed nodes or none at all in any catchment basin.

When the value of the fixed node in the first attracting basin [DB] is the same as the value of the fixed node in the initial state (ex: 1213), which is the unwanted state defined in step S20, the initial In order to change from the state to the desired state of the first attraction, there should be no temporary perturbation of the fixed node.

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

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

In step S330. With respect to only the non-fixed/asymmetric nodes, the Hamming distance between the initial state and the respective states of the desired first attracting basin [DB] may be calculated.

In step S340, the shortest distance among the calculated Hamming distances may be determined, and a set of states having the shortest distance among the states of the first attracting 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 node, symmetric node, and non-fixed/asymmetric nodes are not distinguished from each other, and each state of the initial state and the desired first attraction basin [DB] for all nodes included in the Boolean network. It can be understood that the control node according to the embodiment of the present invention shown in FIG. 11 can be determined even by calculating the Hamming distance between them. However, if the preferred embodiment according to the above-described steps ( S310 , S320 , S330 , S340 ) is not used, the computing power for determining the boundary state will be increased.

The graph shown in FIG. 13 shows the states of the catchment basin of a specific attraction in a network consisting of 21 nodes, and is for explaining the properties of the aforementioned symmetric node.

Numbers 1 to 21 on the horizontal axis of the graph shown in FIG. 13 numerically represent 21 nodes, and each row composed of 21 values indicates different states of the attracting basin, and the dark part of the graph represents 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 having 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' is equal to the number of states whose value is '0'. That is, the average value of the states of the symmetric nodes in the Boolean network is 0.5. It can be seen that the value distribution of the remaining nodes except for the symmetric node is symmetric based on the value of the symmetric node. If the above two properties are satisfied, the node becomes a symmetric node.

Because of the above two properties, the symmetric node 20 is ignored in the initial state, which is not desired, and the Hamming distance from the state of only 20 nodes to the desired attraction can be obtained. 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 above-described temporary perturbation.

14 shows an example of another 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 is ) are all non-fixed/asymmetric nodes.

In the desired attraction basin [DB] of the p53 network 110, the average value of the states of the symmetric nodes is 0.5, the average value of the states of PTEN and P53 among the fixed nodes is 1.0, and PTEN among the fixed nodes and the average value of the states of each node except for P53 is 0.0, and the average values of the states of the non-fixed node are not 0 and 1.0, and the asymmetric node has an average value other than 0.5 or 0.5. The value distribution of the remaining nodes except for the symmetric node is not symmetric with respect to the value of the symmetric node.

As in the above-described method for determining the fixed node, there is no outgoing link from the Proliferation node in the third area 113 . Also, there is one link outgoing from the P21 node and the CyclinD1 node, respectively, and the node connected to this link is a symmetrical proliferation node. And there is one link outgoing from the Bcatenin node, and the node connected to this link is the CyclinD1 node, which is a symmetric node. Accordingly, nodes included in the third region 113 may be determined to be symmetric nodes according to the above definition.

The calculation and comparison of the above-described Hamming distance 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 may represent each node, a dark circle may indicate a state having a value of '1', and a light circle may indicate a state having a value of '0'. . Each node may have an ID between 1 and 21, respectively. The ID for each node is marked inside each circle.

In FIG. 15A , reference numeral 120 denotes the 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 unwanted attraction basin [UB], and reference number 1134 denotes a desired first attractor 1134 belonging to the first attractor basin [DB], which is a desired attractor basin. indicates

In relation to the Boolean network 120 shown in Fig. 15A, it is necessary to first understand the following premise.

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

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

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

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

Fourth, in the Boolean network 120 shown in Fig. 15A, there are two boundary states of the first attracting basin [DB] from the initial state 1214, and the first boundary shown in Figs. 15B and 15C, respectively 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 shows the states of the fixed nodes 5 to 13 and the 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 non-fixed/asymmetric nodes 14, 16, 18, 19, 20 have a value of '1'.

In the first boundary 1127, the values of the fixed nodes 5, 6, 7, 9, 10, 12, 13 and non-fixed/asymmetric nodes 15, 17, 18 are '0', and the fixed nodes 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 is The state changes to the first boundary state 1127, and eventually the state may change to the first attractor 1134, which is an attractor of the first attractor basin [DB] to which the first boundary state 1127 belongs.

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

As described with reference to FIG. 15B , in FIG. 15C , when the states of the initial state 1214 and the second boundary 1128 are compared with each other, only the values of the fixed nodes 6 and 10 and the non-fixed/asymmetric nodes 14 and 21 are these are different 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 is The state is changed to the second boundary state 1128 , and eventually the state may change to the first attractor 1134 , which is the attractor of the first attractor 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 there are a total of two boundary states. In this example, only the first set of nodes consisting of four nodes 6, 10, 18, and 21 is perturbed as shown in FIG. 15B, or as four nodes 6, 10, 14, and 21 as shown in FIG. 15C. By perturbing only the configured second set of nodes, it is possible to change the Boolean network 120 to the desired state of the first attractor 1134 .

Alternatively, even if five or more nodes are perturbed, the initial state 1214 may be changed to an arbitrary state belonging to the first attracting basin [DB]. However, according to the above-described embodiment of the present invention, it is possible to change the desired state of the first attraction 1134 by perturbating only the smallest number of nodes. Each node can mean a different protein, and in order to perturb the state of different proteins together, different drugs may need to be administered together, so by minimizing the number of nodes that need to be perturbed, a good technical effect can be obtained. .

III. Boundary state determination method according to an embodiment of the present invention

16 is a flowchart of a method for determining a boundary state provided according to an embodiment of the present invention.

In step S510, among the nodes of the Boolean network, it is possible to determine a fixed node defined as a node whose value is always constant in all states of the first attraction basin of the Boolean network.

In this case, the first attracting basin may be an attracting basin that does not include an initial state given in advance. That is, the initial state may be a state included in the second attracting basin different from the first attracting basin.

In step S520, a symmetric node may be determined among nodes of the Boolean network.

In this case, the symmetric node may include a structurally symmetric node defined as a node having no outbound link in the structure of the Boolean network.

In this case, the symmetric node may further include another structurally symmetric node having only one outgoing link from the structure of the Boolean network, and the node connected to the outgoing link being the structurally symmetrical node.

In this case, the symmetric node, when the values of the states of the Boolean network are averaged for each node, the average value is 0.5, and further includes a dynamic symmetric node defined as a node in which the remaining states are symmetric with respect to the node. can do.

In step (S530), it is possible to calculate the Hamming distance between the initial state and each state included in the first attraction basin.

In one embodiment, the Hamming distance may be a Hamming distance between the initial state and each state included in the first attraction basin, calculated by targeting only nodes except for the fixed node among the nodes of the Boolean network. have.

In another embodiment, the Hamming distance is calculated for only the nodes excluding the fixed node and the symmetric node among the nodes of the Boolean network, the initial state and each state included in the first attraction basin It may be a hamming distance between them.

In step S540, it may be determined that the state having the shortest Hamming distance from the initial state among the states belonging to the first attracting basin is the boundary state.

IV. Computing device and devices

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

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

The external device 940 may be, for example, a portable recording device such as a 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 a downloadable command code is recorded.

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

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

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 receives from the external device 940 or 960 through the communication interface 930 information about the structure of the Boolean network, information about the initial state of the Boolean network, and the information about the Boolean network. obtain information about a first attractor belonging to a desired first attractor basin that does not include the initial state among attractors, and determine a boundary state of the first attractor basin from the initial state, and the boolean Among the nodes of the Leon network, nodes having different states among the boundary state and the initial state may be determined as a control node. In this case, the boundary state may be a state having a minimum Hamming distance among the Hamming distances between the initial state and each of the states belonging to the first attracting basin among the states belonging to the first attracting basin.

In addition, the processing unit 910 obtains information about the Boolean network from the external device 940 or 960 through the communication interface 930 , and among nodes of the Boolean network, Determine a fixed node defined as a node whose value is always constant in all states of the first attraction basin that does not include a given initial state, and a Hamming distance between the initial state and each state included in the first attractor basin , and it may be configured to determine a state having the shortest Hamming distance from the initial state as a boundary state among states belonging to the first attracting basin. In this case, the Hamming distance may be a Hamming distance between the initial state and each state included in the first attraction basin, calculated for only nodes except for the fixed node among the nodes of the Boolean network.

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-tray 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.

By using the above-described embodiments of the present invention, those skilled in the art will be able to easily implement various changes and modifications within the scope without departing from the essential characteristics of the present invention. The content of each claim in the claims may be combined with other claims without reference within the scope that can be understood through this specification.

Claims (13)

The computing device determines, among the nodes of the Boolean network, a fixed node whose value is defined as a node whose value is always constant in all states of the first attracting basin that does not include a predetermined initial state of the Boolean network. fixed node determination step;
Hamming distance calculation step of calculating, by the computing device, a Hamming distance between the initial state and each state included in the first attraction basin;
determining, by the computing device, a state having a minimum Hamming distance from the initial state among states belonging to the first attraction basin as a boundary state; and
determining, by the computing device, nodes having different states from among the nodes of the Boolean network as control nodes when the boundary state and the initial state are compared with each other;
includes,
The Boolean network is a model of a biomolecule signaling network modeling a dynamic system of a cell, and each node of the Boolean network corresponds to each molecule of the biomolecule signaling network,
The initial state is a state in which the cells are cancer cells,
The first attractor basin is a set of all states included in all state transition paths toward a predetermined first attractor among states that the Boolean network may have,
the control node is a control target node perturbing the biomolecule signaling network to a desired state, and
The Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, which is calculated for only nodes except for the fixed node among the nodes of the Boolean network.
How to determine the boundary state. According to claim 1,
Further comprising the step of determining, by the computing device, a symmetric node among the nodes of the Boolean network,
The symmetric node includes a structurally symmetric node defined as a node having no 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 attraction basin, calculated for only nodes except for the fixed node and the symmetric node among the nodes of the Boolean network,
How to determine the boundary state. The boundary state determination according to claim 2, wherein the symmetric node has only one outgoing link in the structure of the Boolean network, and further comprises another structurally symmetric node in which a node connected to the outgoing link is the structurally symmetric node. Way. The dynamic symmetry of claim 3, 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 is defined as a node in which the remaining states are symmetric with respect to the node. Further comprising a node, boundary state determination method. According to claim 1,
Further comprising the step of determining, by the computing device, a symmetric node among the nodes of the Boolean network,
The symmetric node includes a dynamically 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 symmetric with respect to the node,
The Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, calculated for only nodes except for the fixed node and the symmetric node among the nodes of the Boolean network,
How to determine the boundary state. delete According to claim 1,
The method of determining all states belonging to the first attraction basin is,
obtaining, by the computing device, information about a first attractor belonging to the first chute basin;
initializing, by the computing device, a reference state of the Boolean network to the first decoupling; and
A state tracing step in which the computing device calculates the immediately preceding state of the Boolean network based on ① a first update rule that is an update rule of the state of the Boolean network and ② a reference state of the Boolean network, wherein the reference A state is defined as the state of the Boolean network at a reference time, and the immediately preceding state is defined as the state of the Boolean network at a time immediately preceding the reference time.
includes,
For each of the calculated immediately preceding states, after updating the reference state to the calculated immediately preceding state and repeating the state backtracking step, determining all states of the first attractor basin including the first attractor characterized by,
How to determine the boundary state. 8. The method of claim 7,
Among the calculated immediate states, those determined to be terminal states are not qualified as the state of the Boolean network at the reference time, and the state traceback 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 boundary state. 8. The method of claim 7,
The boolean network is a symmetric node removed from the first boolean network,
The first attraction of the Boolean network is characterized in that the value of the removed symmetric node is removed from a specific attraction of the first Boolean network,
How to determine the boundary state. delete A computing device comprising a communication interface and a processing unit for communicating with an external device by wire or wirelessly,
The processing unit,
Obtaining information about the Boolean network from the external device through the communication interface,
determining, among the nodes of the Boolean network, a fixed node defined as a node whose value is always constant in all states of a first attracting basin that does not include a given initial state of the Boolean network;
Calculate the Hamming distance between the initial state and each state included in the first attraction basin,
and to determine that a state having a minimum Hamming distance from the initial state among states belonging to the first attracting basin is a boundary state, and
Among the nodes of the Boolean network, when the boundary state and the initial state are compared with each other, nodes having different states are determined as control nodes,
The Boolean network is a model of a biomolecule signaling network modeling a dynamic system of a cell, and each node of the Boolean network corresponds to each molecule of the biomolecule signaling network,
The initial state is a state in which the cells are cancer cells,
The first attraction basin is a set of all states included in all state transition paths toward a predetermined first attraction among states that the Boolean network may have,
the control node is a control target node for perturbing the biomolecule signaling network to a desired state, and
The Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, which is calculated for only nodes except for the fixed node among the nodes of the Boolean network.
computing device. The processing unit of the computing device including a communication interface and processing unit for communicating with an external device by wire or wirelessly,
obtaining information about a Boolean network from the external device through the communication interface;
A fixed node determination step of determining, among the nodes of the Boolean network, a fixed node defined as a node whose value is always constant in all states of the first attraction not including the given initial state of the Boolean network ;
calculating a Hamming distance between the initial state and each state included in the first attraction basin;
determining a state having a minimum Hamming distance from the initial state among states belonging to the first attraction basin as a boundary state; and
determining, among nodes of the Boolean network, nodes having different states when the boundary state and the initial state are compared with each other as control nodes;
A computer-readable non-transitory storage device in which a program to run is recorded,
The Boolean network is a model of a biomolecule signaling network modeling a dynamic system of a cell, and each node of the Boolean network corresponds to each molecule of the biomolecule signaling network,
The initial state is a state in which the cells are cancer cells,
The first attraction basin is a set of all states included in all state transition paths toward a predetermined first attraction among states that the Boolean network may have,
the control node is a control target node for perturbing the biomolecule signaling network to a desired state, and
The Hamming distance is a Hamming distance between the initial state and each state included in the first attraction basin, which is calculated for only nodes except for the fixed node among the nodes of the Boolean network.
Computer-readable, non-transitory storage. delete

Images