dorsal/arxiv
View SchemaMonotone and near-monotone network structure (part II)
| Authors | Eduardo D. Sontag |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0612033 |
| URL | https://arxiv.org/abs/q-bio/0612033 |
Abstract
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from signed network structure, associated to purely stoichiometric information and ignoring fluxes. In particular, monotone systems respond in a predictable fashion to perturbations and have robust and ordered dynamical characteristics, making them reliable components of larger networks. Interconnections of monotone systems may be fruitfully analyzed using tools from control theory, by viewing larger systems as interconnections of monotone subsystems. This allows one to obtain precise bifurcation diagrams without appeal to explicit knowledge of fluxes or of kinetic constants and other parameters, using merely "input/output characteristics" (steady-state responses or DC gains). The procedure may be viewed as a "model reduction" approach in which monotone subsystems are viewed as essentially one-dimensional objects. The possibility of performing a decomposition into a small number of monotone components is closely tied to the question of how "near" a system is to being monotone. We argue that systems that are "near monotone" may be more biologically more desirable than systems that are far from being monotone. Indeed, there are indications that biological networks may be much closer to being monotone than random networks that have the same numbers of vertices and of positive and negative edges.
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"abstract": "This paper (parts I and II) provides an expository introduction to monotone\nand near-monotone dynamical systems associated to biochemical networks, those\nwhose graphs are consistent or near-consistent. Many conclusions can be drawn\nfrom signed network structure, associated to purely stoichiometric information\nand ignoring fluxes. In particular, monotone systems respond in a predictable\nfashion to perturbations and have robust and ordered dynamical characteristics,\nmaking them reliable components of larger networks. Interconnections of\nmonotone systems may be fruitfully analyzed using tools from control theory, by\nviewing larger systems as interconnections of monotone subsystems. This allows\none to obtain precise bifurcation diagrams without appeal to explicit knowledge\nof fluxes or of kinetic constants and other parameters, using merely\n\"input/output characteristics\" (steady-state responses or DC gains). The\nprocedure may be viewed as a \"model reduction\" approach in which monotone\nsubsystems are viewed as essentially one-dimensional objects. The possibility\nof performing a decomposition into a small number of monotone components is\nclosely tied to the question of how \"near\" a system is to being monotone. We\nargue that systems that are \"near monotone\" may be more biologically more\ndesirable than systems that are far from being monotone. Indeed, there are\nindications that biological networks may be much closer to being monotone than\nrandom networks that have the same numbers of vertices and of positive and\nnegative edges.",
"arxiv_id": "q-bio/0612033",
"authors": [
"Eduardo D. Sontag"
],
"categories": [
"q-bio.MN",
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"title": "Monotone and near-monotone network structure (part II)",
"url": "https://arxiv.org/abs/q-bio/0612033"
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