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Monotone and near-monotone biochemical networks.

Sontag ED - Syst Synth Biol (2007)

Bottom Line: Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations.This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a "small" number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory.This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion.

View Article: PubMed Central - PubMed

Affiliation: Rutgers University, New Brunswick, NJ, USA, sontag@math.rutgers.edu.

ABSTRACT
Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a "small" number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion.

No MeSH data available.


(a) inconsistent, (b) consistent, (c) adding node to consistent network
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Fig5: (a) inconsistent, (b) consistent, (c) adding node to consistent network

Mentions: Consistent graphs can be embedded into larger consistent ones, but inconsistent ones cannot. For example, consider the graph shown in Fig. 5a. This graph admits no consistent spin assignment since the undirected loop 1,3,4,2,1 has a net negative parity. Thus, there cannot be any consistent graph that includes this graph as a subgraph. Compare this with the graph shown in Fig. 5b. Consistency of this graph may well represent consistency of a larger graph which involves a yet-undiscovered species, such as node 5 in Fig. 5c. Alternatively, and from an “incremental design” viewpoint, this graph being consistent makes it possible to consistently add node 5 in the future.Fig. 5


Monotone and near-monotone biochemical networks.

Sontag ED - Syst Synth Biol (2007)

(a) inconsistent, (b) consistent, (c) adding node to consistent network
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2533521&req=5

Fig5: (a) inconsistent, (b) consistent, (c) adding node to consistent network
Mentions: Consistent graphs can be embedded into larger consistent ones, but inconsistent ones cannot. For example, consider the graph shown in Fig. 5a. This graph admits no consistent spin assignment since the undirected loop 1,3,4,2,1 has a net negative parity. Thus, there cannot be any consistent graph that includes this graph as a subgraph. Compare this with the graph shown in Fig. 5b. Consistency of this graph may well represent consistency of a larger graph which involves a yet-undiscovered species, such as node 5 in Fig. 5c. Alternatively, and from an “incremental design” viewpoint, this graph being consistent makes it possible to consistently add node 5 in the future.Fig. 5

Bottom Line: Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations.This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a "small" number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory.This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion.

View Article: PubMed Central - PubMed

Affiliation: Rutgers University, New Brunswick, NJ, USA, sontag@math.rutgers.edu.

ABSTRACT
Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a "small" number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion.

No MeSH data available.