The Power-law formalism as a tool for modeling hormonal systems

Modeling a hormone system requires a number of simplifying assumptions. Often, the final conceptual model incorporates a number of aggregated processes that have no correspondence with a single enzyme-catalyzed reaction. In such cases, it is discussible using models based on classical biochemical ki...

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Autores: Sorribas Tello, Albert, González Sistal, Ángel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:1999
País:España
Recursos:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/71572
Acesso em linha:https://doi.org/10.1080/17486709909490786
http://hdl.handle.net/10459.1/71572
Access Level:acceso abierto
Palavra-chave:Hormone system
Mathematical model
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spelling The Power-law formalism as a tool for modeling hormonal systemsSorribas Tello, AlbertGonzález Sistal, ÁngelHormone systemMathematical modelModeling a hormone system requires a number of simplifying assumptions. Often, the final conceptual model incorporates a number of aggregated processes that have no correspondence with a single enzyme-catalyzed reaction. In such cases, it is discussible using models based on classical biochemical kinetics rate laws that are valid only under specific conditions. The power-law formalism provides an alternative framework for building up a mathematical model in such cases. The resulting model is a set of ordinary differential equations with a special structure that allows efficient symbolic and numerical analysis of the system’s properties. In these equations, the underlying rate-laws of each of the component processes are represented by a power-law that is an exact representation of the actual rate-law at the operating point. The particular form of these equations allows representation of a wide range of kinetic features without changing the basic power-law form. Moreover, its parameters have an immediate interpretation as apparent kinetic- orders and rate-constants. This is especially helpful for incorporating both quantitative and qualitative information in the process of model definition. This is particularly useful when detailed kinetic information concerning system’s components is not available. In this paper we show the utility of the power-law approach in this context by deriving an illustrative model of a complex physiological system: the hypothalamus-anterior pituitary- thyroid network. First, we derive a conceptual model that incorporates the key features of this system. Then, we derive an S-system model, one of the preferred variants within the power-law formalism, and we show its utility in exploring the system properties. The model qualitatively reproduces the response of normal, hyperthyroid, and hypothyroid patients to a clinical test involving a thyrotropin releasing hormone injection. Finally, we illustrate the utility of this modeling strategy for studying the system’s response to different dynamic patterns of regulatory signals, and for exploring how altered dynamic patterns of stimulatory signals can cause pathological states.Hindawi1999info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1080/17486709909490786http://hdl.handle.net/10459.1/71572reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésReproducció del document publicat a: https://doi.org/10.1080/17486709909490786Computational and Mathematical Methods in Medicine, vol. 2, art. 258170cc-by (c) OPA (Overseas Publishera Aasociation), 1999cc-by (c) Hindawi Publishing Corporation, 1999info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:repositori.udl.cat:10459.1/715722026-06-24T12:42:17Z
dc.title.none.fl_str_mv The Power-law formalism as a tool for modeling hormonal systems
title The Power-law formalism as a tool for modeling hormonal systems
spellingShingle The Power-law formalism as a tool for modeling hormonal systems
Sorribas Tello, Albert
Hormone system
Mathematical model
title_short The Power-law formalism as a tool for modeling hormonal systems
title_full The Power-law formalism as a tool for modeling hormonal systems
title_fullStr The Power-law formalism as a tool for modeling hormonal systems
title_full_unstemmed The Power-law formalism as a tool for modeling hormonal systems
title_sort The Power-law formalism as a tool for modeling hormonal systems
dc.creator.none.fl_str_mv Sorribas Tello, Albert
González Sistal, Ángel
author Sorribas Tello, Albert
author_facet Sorribas Tello, Albert
González Sistal, Ángel
author_role author
author2 González Sistal, Ángel
author2_role author
dc.subject.none.fl_str_mv Hormone system
Mathematical model
topic Hormone system
Mathematical model
description Modeling a hormone system requires a number of simplifying assumptions. Often, the final conceptual model incorporates a number of aggregated processes that have no correspondence with a single enzyme-catalyzed reaction. In such cases, it is discussible using models based on classical biochemical kinetics rate laws that are valid only under specific conditions. The power-law formalism provides an alternative framework for building up a mathematical model in such cases. The resulting model is a set of ordinary differential equations with a special structure that allows efficient symbolic and numerical analysis of the system’s properties. In these equations, the underlying rate-laws of each of the component processes are represented by a power-law that is an exact representation of the actual rate-law at the operating point. The particular form of these equations allows representation of a wide range of kinetic features without changing the basic power-law form. Moreover, its parameters have an immediate interpretation as apparent kinetic- orders and rate-constants. This is especially helpful for incorporating both quantitative and qualitative information in the process of model definition. This is particularly useful when detailed kinetic information concerning system’s components is not available. In this paper we show the utility of the power-law approach in this context by deriving an illustrative model of a complex physiological system: the hypothalamus-anterior pituitary- thyroid network. First, we derive a conceptual model that incorporates the key features of this system. Then, we derive an S-system model, one of the preferred variants within the power-law formalism, and we show its utility in exploring the system properties. The model qualitatively reproduces the response of normal, hyperthyroid, and hypothyroid patients to a clinical test involving a thyrotropin releasing hormone injection. Finally, we illustrate the utility of this modeling strategy for studying the system’s response to different dynamic patterns of regulatory signals, and for exploring how altered dynamic patterns of stimulatory signals can cause pathological states.
publishDate 1999
dc.date.none.fl_str_mv 1999
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1080/17486709909490786
http://hdl.handle.net/10459.1/71572
url https://doi.org/10.1080/17486709909490786
http://hdl.handle.net/10459.1/71572
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1080/17486709909490786
Computational and Mathematical Methods in Medicine, vol. 2, art. 258170
dc.rights.none.fl_str_mv cc-by (c) OPA (Overseas Publishera Aasociation), 1999
cc-by (c) Hindawi Publishing Corporation, 1999
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
rights_invalid_str_mv cc-by (c) OPA (Overseas Publishera Aasociation), 1999
cc-by (c) Hindawi Publishing Corporation, 1999
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Hindawi
publisher.none.fl_str_mv Hindawi
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
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repository.mail.fl_str_mv
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