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Identifying dynamical modules from genetic regulatory systems: applications to the segment polarity network.

Irons DJ, Monk NA - BMC Bioinformatics (2007)

Bottom Line: We have designed a technique for decomposing any set of discrete-state, discrete-time attractors into subsystems.Having a suitable mathematical model also allows us to describe how each subsystem is regulated and how robust each subsystem is against perturbations.However, since the subsystems are found directly from the attractors, a mathematical model or underlying network topology is not necessarily required to identify them, potentially allowing the method to be applied directly to experimental expression data.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Computer Science, University of Sheffield, UK. d.irons@sheffield.ac.uk

ABSTRACT

Background: It is widely accepted that genetic regulatory systems are 'modular', in that the whole system is made up of smaller 'subsystems' corresponding to specific biological functions. Most attempts to identify modules in genetic regulatory systems have relied on the topology of the underlying network. However, it is the temporal activity (dynamics) of genes and proteins that corresponds to biological functions, and hence it is dynamics that we focus on here for identifying subsystems.

Results: Using Boolean network models as an exemplar, we present a new technique to identify subsystems, based on their dynamical properties. The main part of the method depends only on the stable dynamics (attractors) of the system, thus requiring no prior knowledge of the underlying network. However, knowledge of the logical relationships between the network components can be used to describe how each subsystem is regulated. To demonstrate its applicability to genetic regulatory systems, we apply the method to a model of the Drosophila segment polarity network, providing a detailed breakdown of the system.

Conclusion: We have designed a technique for decomposing any set of discrete-state, discrete-time attractors into subsystems. Having a suitable mathematical model also allows us to describe how each subsystem is regulated and how robust each subsystem is against perturbations. However, since the subsystems are found directly from the attractors, a mathematical model or underlying network topology is not necessarily required to identify them, potentially allowing the method to be applied directly to experimental expression data.

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Identifying Intersection sequences. Every path from left to right (starting at '-') in this tree represents a different node set N ⊆ V = {n1, n2, n3, n4, n5}. It is possible to search this tree and visit every node set N ⊆ V (exactly once). For example, follow the path {n1} → {n1, n2} → {n1, n2, n3} → {n1, n2, n3, n4} → {n1, n2, n3, n4, n5} → {n1, n2, n3, n5} → {n1, n2, n4} → {n1, n2, n4, n5} → {n1, n2, n5} → {n1, n3} → {n1, n3, n4} → {n1, n3, n4, n5} → {n1, n3, n5} → {n1, n4} → {n1, n4, n5} → {n1, n5} → {n2} → {n2, n3} → {n2, n3, n4} → {n2, n3, n4, n5} → {n2, n3, n5} → {n2, n4} → {n2, n4, n5} → {n2, n5} → {n3} → {n3, n4} → {n3, n4, n5} → {n3, n5} → {n4} → {n4, n5} → {n5}
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Figure 8: Identifying Intersection sequences. Every path from left to right (starting at '-') in this tree represents a different node set N ⊆ V = {n1, n2, n3, n4, n5}. It is possible to search this tree and visit every node set N ⊆ V (exactly once). For example, follow the path {n1} → {n1, n2} → {n1, n2, n3} → {n1, n2, n3, n4} → {n1, n2, n3, n4, n5} → {n1, n2, n3, n5} → {n1, n2, n4} → {n1, n2, n4, n5} → {n1, n2, n5} → {n1, n3} → {n1, n3, n4} → {n1, n3, n4, n5} → {n1, n3, n5} → {n1, n4} → {n1, n4, n5} → {n1, n5} → {n2} → {n2, n3} → {n2, n3, n4} → {n2, n3, n4, n5} → {n2, n3, n5} → {n2, n4} → {n2, n4, n5} → {n2, n5} → {n3} → {n3, n4} → {n3, n4, n5} → {n3, n5} → {n4} → {n4, n5} → {n5}

Mentions: The method for identifying every intersection sequence can be visualised by considering the tree in Fig. 8. Searching through a tree analogous to this one (for a network with nodes V = {n1, ..., nv}), means that every node set N can be visited at some point. Then, using Procedure 2, we can identify the partial state sequences that occur in each attractor (for each node set N). Then, after the tree has been fully examined, we can pick out the partial state sequences (P) and sets of attractors that satisfy the 3 properties of Definition 4. In reality, many branches of the tree can be ignored, leading to improvements in efficiency (discussed below).


Identifying dynamical modules from genetic regulatory systems: applications to the segment polarity network.

Irons DJ, Monk NA - BMC Bioinformatics (2007)

Identifying Intersection sequences. Every path from left to right (starting at '-') in this tree represents a different node set N ⊆ V = {n1, n2, n3, n4, n5}. It is possible to search this tree and visit every node set N ⊆ V (exactly once). For example, follow the path {n1} → {n1, n2} → {n1, n2, n3} → {n1, n2, n3, n4} → {n1, n2, n3, n4, n5} → {n1, n2, n3, n5} → {n1, n2, n4} → {n1, n2, n4, n5} → {n1, n2, n5} → {n1, n3} → {n1, n3, n4} → {n1, n3, n4, n5} → {n1, n3, n5} → {n1, n4} → {n1, n4, n5} → {n1, n5} → {n2} → {n2, n3} → {n2, n3, n4} → {n2, n3, n4, n5} → {n2, n3, n5} → {n2, n4} → {n2, n4, n5} → {n2, n5} → {n3} → {n3, n4} → {n3, n4, n5} → {n3, n5} → {n4} → {n4, n5} → {n5}
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Figure 8: Identifying Intersection sequences. Every path from left to right (starting at '-') in this tree represents a different node set N ⊆ V = {n1, n2, n3, n4, n5}. It is possible to search this tree and visit every node set N ⊆ V (exactly once). For example, follow the path {n1} → {n1, n2} → {n1, n2, n3} → {n1, n2, n3, n4} → {n1, n2, n3, n4, n5} → {n1, n2, n3, n5} → {n1, n2, n4} → {n1, n2, n4, n5} → {n1, n2, n5} → {n1, n3} → {n1, n3, n4} → {n1, n3, n4, n5} → {n1, n3, n5} → {n1, n4} → {n1, n4, n5} → {n1, n5} → {n2} → {n2, n3} → {n2, n3, n4} → {n2, n3, n4, n5} → {n2, n3, n5} → {n2, n4} → {n2, n4, n5} → {n2, n5} → {n3} → {n3, n4} → {n3, n4, n5} → {n3, n5} → {n4} → {n4, n5} → {n5}
Mentions: The method for identifying every intersection sequence can be visualised by considering the tree in Fig. 8. Searching through a tree analogous to this one (for a network with nodes V = {n1, ..., nv}), means that every node set N can be visited at some point. Then, using Procedure 2, we can identify the partial state sequences that occur in each attractor (for each node set N). Then, after the tree has been fully examined, we can pick out the partial state sequences (P) and sets of attractors that satisfy the 3 properties of Definition 4. In reality, many branches of the tree can be ignored, leading to improvements in efficiency (discussed below).

Bottom Line: We have designed a technique for decomposing any set of discrete-state, discrete-time attractors into subsystems.Having a suitable mathematical model also allows us to describe how each subsystem is regulated and how robust each subsystem is against perturbations.However, since the subsystems are found directly from the attractors, a mathematical model or underlying network topology is not necessarily required to identify them, potentially allowing the method to be applied directly to experimental expression data.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Computer Science, University of Sheffield, UK. d.irons@sheffield.ac.uk

ABSTRACT

Background: It is widely accepted that genetic regulatory systems are 'modular', in that the whole system is made up of smaller 'subsystems' corresponding to specific biological functions. Most attempts to identify modules in genetic regulatory systems have relied on the topology of the underlying network. However, it is the temporal activity (dynamics) of genes and proteins that corresponds to biological functions, and hence it is dynamics that we focus on here for identifying subsystems.

Results: Using Boolean network models as an exemplar, we present a new technique to identify subsystems, based on their dynamical properties. The main part of the method depends only on the stable dynamics (attractors) of the system, thus requiring no prior knowledge of the underlying network. However, knowledge of the logical relationships between the network components can be used to describe how each subsystem is regulated. To demonstrate its applicability to genetic regulatory systems, we apply the method to a model of the Drosophila segment polarity network, providing a detailed breakdown of the system.

Conclusion: We have designed a technique for decomposing any set of discrete-state, discrete-time attractors into subsystems. Having a suitable mathematical model also allows us to describe how each subsystem is regulated and how robust each subsystem is against perturbations. However, since the subsystems are found directly from the attractors, a mathematical model or underlying network topology is not necessarily required to identify them, potentially allowing the method to be applied directly to experimental expression data.

Show MeSH