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Activating and inhibiting connections in biological network dynamics.

McDonald D, Waterbury L, Knight R, Betterton MD - Biol. Direct (2008)

Bottom Line: However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein).For the full reviews, please go to the Reviewers' comments section.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Physics, University of Colorado, 390 UCB, Boulder, CO 80309, USA. daniel.mcdonald@colorado.edu

ABSTRACT

Background: Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.

Results: Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.

Conclusion: The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.

Reviewers: Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

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Related in: MedlinePlus

Example networks and dynamics. A and B: sketches of 3-node networks. Numbered points represent nodes and arrows interactions; blue/red arrows show activating/inhibiting connections. The interaction strength is given next to each arrow. The two networks have the same topology but differ in connection strengths and activating fraction of connections a; B shows a lower a. C and D: matrices W which represent networks A and B, where Wij is the interaction strength from node j to node i. E and F: Network dynamics with initial condition s(t = 0) = (1, -1, 1). Active/inactive nodes are represented by yellow/black squares The activity of network A reaches steady state after 2 iterations (E). The activity of network B undergoes period-3 oscillation (F).
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Figure 1: Example networks and dynamics. A and B: sketches of 3-node networks. Numbered points represent nodes and arrows interactions; blue/red arrows show activating/inhibiting connections. The interaction strength is given next to each arrow. The two networks have the same topology but differ in connection strengths and activating fraction of connections a; B shows a lower a. C and D: matrices W which represent networks A and B, where Wij is the interaction strength from node j to node i. E and F: Network dynamics with initial condition s(t = 0) = (1, -1, 1). Active/inactive nodes are represented by yellow/black squares The activity of network A reaches steady state after 2 iterations (E). The activity of network B undergoes period-3 oscillation (F).

Mentions: Our model includes key features of a biochemical network: interactions of varying strengths, strongly nonlinear dynamics, and saturating response to inputs [15]. Variants of the model have been used to study robustness in genetic networks, with a focus on dynamics that reach steady state [18-21]. The model describes interactions among the nodes – which represent the genes, mRNA transcripts, or proteins – and the activity of each node – which represents the expression and/or activity level of the molecule. (Activity of a molecule changes if its concentration changes, or because of chemical changes such as phosphorylation.) The interaction strengths are given by the matrix W, where Wij is the strength of the effect of node j on node i (fig. 1). Each Wij can be positive (activating), negative (inhibiting), or zero (no interaction). The activating fraction a is the fraction of nonzero interaction strengths which are positive. Nodes can self-regulate, an effect known to be important in biochemical networks [22,23]. The activity vector is s, with si the activity of node i. Each si is between -1 ("off") and 1 ("on"), where 0 corresponds to the basal activity of the node. This model is similar to a class of models of neuronal networks [24], where the balance of activating and inhibiting connections is also of interest [25-27].


Activating and inhibiting connections in biological network dynamics.

McDonald D, Waterbury L, Knight R, Betterton MD - Biol. Direct (2008)

Example networks and dynamics. A and B: sketches of 3-node networks. Numbered points represent nodes and arrows interactions; blue/red arrows show activating/inhibiting connections. The interaction strength is given next to each arrow. The two networks have the same topology but differ in connection strengths and activating fraction of connections a; B shows a lower a. C and D: matrices W which represent networks A and B, where Wij is the interaction strength from node j to node i. E and F: Network dynamics with initial condition s(t = 0) = (1, -1, 1). Active/inactive nodes are represented by yellow/black squares The activity of network A reaches steady state after 2 iterations (E). The activity of network B undergoes period-3 oscillation (F).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2651858&req=5

Figure 1: Example networks and dynamics. A and B: sketches of 3-node networks. Numbered points represent nodes and arrows interactions; blue/red arrows show activating/inhibiting connections. The interaction strength is given next to each arrow. The two networks have the same topology but differ in connection strengths and activating fraction of connections a; B shows a lower a. C and D: matrices W which represent networks A and B, where Wij is the interaction strength from node j to node i. E and F: Network dynamics with initial condition s(t = 0) = (1, -1, 1). Active/inactive nodes are represented by yellow/black squares The activity of network A reaches steady state after 2 iterations (E). The activity of network B undergoes period-3 oscillation (F).
Mentions: Our model includes key features of a biochemical network: interactions of varying strengths, strongly nonlinear dynamics, and saturating response to inputs [15]. Variants of the model have been used to study robustness in genetic networks, with a focus on dynamics that reach steady state [18-21]. The model describes interactions among the nodes – which represent the genes, mRNA transcripts, or proteins – and the activity of each node – which represents the expression and/or activity level of the molecule. (Activity of a molecule changes if its concentration changes, or because of chemical changes such as phosphorylation.) The interaction strengths are given by the matrix W, where Wij is the strength of the effect of node j on node i (fig. 1). Each Wij can be positive (activating), negative (inhibiting), or zero (no interaction). The activating fraction a is the fraction of nonzero interaction strengths which are positive. Nodes can self-regulate, an effect known to be important in biochemical networks [22,23]. The activity vector is s, with si the activity of node i. Each si is between -1 ("off") and 1 ("on"), where 0 corresponds to the basal activity of the node. This model is similar to a class of models of neuronal networks [24], where the balance of activating and inhibiting connections is also of interest [25-27].

Bottom Line: However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein).For the full reviews, please go to the Reviewers' comments section.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Physics, University of Colorado, 390 UCB, Boulder, CO 80309, USA. daniel.mcdonald@colorado.edu

ABSTRACT

Background: Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.

Results: Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.

Conclusion: The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.

Reviewers: Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

Show MeSH
Related in: MedlinePlus