dorsal/arxiv
View SchemaMathematical approaches to differentiation and gene regulation
| Authors | C. Soulé |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0510027 |
| URL | https://arxiv.org/abs/q-bio/0510027 |
Abstract
We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. Once such a graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. In this paper we discuss a rule proposed by R.Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential or boolean type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models and the corresponding discrete models. We discuss open problems as well.
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"abstract": "We consider some mathematical issues raised by the modelling of gene\nnetworks. The expression of genes is governed by a complex set of regulations,\nwhich is often described symbolically by interaction graphs. Once such a graph\nhas been established, there remains the difficult task to decide which\ndynamical properties of the gene network can be inferred from it, in the\nabsence of precise quantitative data about their regulation. In this paper we\ndiscuss a rule proposed by R.Thomas according to which the possibility for the\nnetwork to have several stationary states implies the existence of a positive\ncircuit in the corresponding interaction graph. We prove that, when properly\nformulated in rigorous terms, this rule becomes a theorem valid for several\ndifferent types of formal models of gene networks. This result is already known\nfor models of differential or boolean type. We show here that a stronger\nversion of it holds in the differential setup when the decay of protein\nconcentrations is taken into account. This allows us to verify also the\nvalidity of Thomas\u0027 rule in the context of piecewise-linear models and the\ncorresponding discrete models. We discuss open problems as well.",
"arxiv_id": "q-bio/0510027",
"authors": [
"C. Soul\u00e9"
],
"categories": [
"q-bio.MN"
],
"title": "Mathematical approaches to differentiation and gene regulation",
"url": "https://arxiv.org/abs/q-bio/0510027"
},
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