# On the Use of the Hill Functions in Mathematical Models of Gene Regulatory Networks

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 2, page 85-97
- ISSN: 0973-5348

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topSantillán, M.. "On the Use of the Hill Functions in Mathematical Models of Gene Regulatory Networks." Mathematical Modelling of Natural Phenomena 3.2 (2008): 85-97. <http://eudml.org/doc/222194>.

@article{Santillán2008,

abstract = {
Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneously
bind a single receptor. This result if often employed to interpret the Hill coefficient as
the number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibrium
states of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively and
in a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate,
but only an upper bound, for the Hill coefficient; while the Hill coefficient depends quite strongly
on the cooperativity level among ligands. We finally use these results to discuss the feasibility
and constrains of using Hill functions to model the regulatory functions in mathematical models of
gene regulatory networks.
},

author = {Santillán, M.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {systems biology; molecular biology; cooperativity; Hill coefficient},

language = {eng},

month = {10},

number = {2},

pages = {85-97},

publisher = {EDP Sciences},

title = {On the Use of the Hill Functions in Mathematical Models of Gene Regulatory Networks},

url = {http://eudml.org/doc/222194},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Santillán, M.

TI - On the Use of the Hill Functions in Mathematical Models of Gene Regulatory Networks

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/10//

PB - EDP Sciences

VL - 3

IS - 2

SP - 85

EP - 97

AB -
Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneously
bind a single receptor. This result if often employed to interpret the Hill coefficient as
the number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibrium
states of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively and
in a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate,
but only an upper bound, for the Hill coefficient; while the Hill coefficient depends quite strongly
on the cooperativity level among ligands. We finally use these results to discuss the feasibility
and constrains of using Hill functions to model the regulatory functions in mathematical models of
gene regulatory networks.

LA - eng

KW - systems biology; molecular biology; cooperativity; Hill coefficient

UR - http://eudml.org/doc/222194

ER -

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