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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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Partition sequences in the example Boolean network model. (A) 10 partition sequences are identified for the example model in Fig. 2. Each column in each sequence corresponds to a node in the model, whilst each row corresponds to a partial state. White/Black corresponds to the node having state 1/0 in the partial state. Eight of these (P3 – P10) are also intersection sequences, whilst the remaining two (P1 and P2, starred) are core sequences that underlie multiple intersection sequences (see Tables 1 and 2). (B, C) Examples of hierarchy amongst the sequences in A. In each case, node i corresponds to the partial state sequence Pi. In each case, if a link joins a partial state sequence Px (top) to another Py (bottom), Px occurs in Py and is conserved across a greater number of attractors. (B) Hierarchy between intersection sequences. (C) Hierarchy between partition sequences. Orange nodes correspond to sequences with sub-dynamics that are distinct from those in sequences further up the hierarchy. These 6 distinct sub-dynamics are the subsystems (see Table 3). White nodes correspond to sequences that are just a combination of sequences further up the hierarchy.
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Figure 3: Partition sequences in the example Boolean network model. (A) 10 partition sequences are identified for the example model in Fig. 2. Each column in each sequence corresponds to a node in the model, whilst each row corresponds to a partial state. White/Black corresponds to the node having state 1/0 in the partial state. Eight of these (P3 – P10) are also intersection sequences, whilst the remaining two (P1 and P2, starred) are core sequences that underlie multiple intersection sequences (see Tables 1 and 2). (B, C) Examples of hierarchy amongst the sequences in A. In each case, node i corresponds to the partial state sequence Pi. In each case, if a link joins a partial state sequence Px (top) to another Py (bottom), Px occurs in Py and is conserved across a greater number of attractors. (B) Hierarchy between intersection sequences. (C) Hierarchy between partition sequences. Orange nodes correspond to sequences with sub-dynamics that are distinct from those in sequences further up the hierarchy. These 6 distinct sub-dynamics are the subsystems (see Table 3). White nodes correspond to sequences that are just a combination of sequences further up the hierarchy.

Mentions: The new method of identifying subsystems is a two stage process that breaks up the system's attractors, to leave partial state sequences that are optimally distinguishable from one another. A summary of these two stages, along with relevant definitions, is given below using the simple example in Fig. 2 and Fig. 3. Detailed descriptions of the algorithms are given in the Methods section for those wanting to implement this method. A flow diagram of the procedures involved can be seen in Fig. 1


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

Irons DJ, Monk NA - BMC Bioinformatics (2007)

Partition sequences in the example Boolean network model. (A) 10 partition sequences are identified for the example model in Fig. 2. Each column in each sequence corresponds to a node in the model, whilst each row corresponds to a partial state. White/Black corresponds to the node having state 1/0 in the partial state. Eight of these (P3 – P10) are also intersection sequences, whilst the remaining two (P1 and P2, starred) are core sequences that underlie multiple intersection sequences (see Tables 1 and 2). (B, C) Examples of hierarchy amongst the sequences in A. In each case, node i corresponds to the partial state sequence Pi. In each case, if a link joins a partial state sequence Px (top) to another Py (bottom), Px occurs in Py and is conserved across a greater number of attractors. (B) Hierarchy between intersection sequences. (C) Hierarchy between partition sequences. Orange nodes correspond to sequences with sub-dynamics that are distinct from those in sequences further up the hierarchy. These 6 distinct sub-dynamics are the subsystems (see Table 3). White nodes correspond to sequences that are just a combination of sequences further up the hierarchy.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC2233651&req=5

Figure 3: Partition sequences in the example Boolean network model. (A) 10 partition sequences are identified for the example model in Fig. 2. Each column in each sequence corresponds to a node in the model, whilst each row corresponds to a partial state. White/Black corresponds to the node having state 1/0 in the partial state. Eight of these (P3 – P10) are also intersection sequences, whilst the remaining two (P1 and P2, starred) are core sequences that underlie multiple intersection sequences (see Tables 1 and 2). (B, C) Examples of hierarchy amongst the sequences in A. In each case, node i corresponds to the partial state sequence Pi. In each case, if a link joins a partial state sequence Px (top) to another Py (bottom), Px occurs in Py and is conserved across a greater number of attractors. (B) Hierarchy between intersection sequences. (C) Hierarchy between partition sequences. Orange nodes correspond to sequences with sub-dynamics that are distinct from those in sequences further up the hierarchy. These 6 distinct sub-dynamics are the subsystems (see Table 3). White nodes correspond to sequences that are just a combination of sequences further up the hierarchy.
Mentions: The new method of identifying subsystems is a two stage process that breaks up the system's attractors, to leave partial state sequences that are optimally distinguishable from one another. A summary of these two stages, along with relevant definitions, is given below using the simple example in Fig. 2 and Fig. 3. Detailed descriptions of the algorithms are given in the Methods section for those wanting to implement this method. A flow diagram of the procedures involved can be seen in Fig. 1

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