Kinetic interpretation of log-logistic dose-time response curves

Abstract A Hill-type time-response curve was derived using a single-step chemical kinetics approximation. The rate expression for the transformation is a differential equation that provides an interpolation formula between the logistic growth curve and second order kinetics. The solution is equivale...

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Autores principales:	Walter W. Focke, Isbe van der Westhuizen, Ndeke Musee, Mattheüs Theodor Loots
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/5f95e45c60be4a42ab70ecd2253f8e8c
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spelling	oai:doaj.org-article:5f95e45c60be4a42ab70ecd2253f8e8c2021-12-02T12:30:35ZKinetic interpretation of log-logistic dose-time response curves10.1038/s41598-017-02474-w2045-2322https://doaj.org/article/5f95e45c60be4a42ab70ecd2253f8e8c2017-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-02474-whttps://doaj.org/toc/2045-2322Abstract A Hill-type time-response curve was derived using a single-step chemical kinetics approximation. The rate expression for the transformation is a differential equation that provides an interpolation formula between the logistic growth curve and second order kinetics. The solution is equivalent to the log-logistic cumulative distribution function with the time constant expressed in terms of a kinetic rate constant. This expression was extended to a full dose-time-response equation by postulating a concentration dependence for the rate constant. This was achieved by invoking a modified form of Haber’s law that connects an observed toxic effect with the concentration of the active agent and the elapsed exposure time. Analysis showed that the concept of Concentration Addition corresponds to a special case where the rate constant for the overall transformation rate is proportional to the sum of the rate constants that apply when the agents act individually. Biodiesel “survival” curves were measured and used to test the applicability of the empirical model to describe the effects of inhibitor dosage and binary inhibitor mixtures. Positive results suggest that the proposed dose-response relationship for the toxicity of agents to organisms can be extended to inanimate systems especially in cases where accurate mechanistic models are lacking.Walter W. FockeIsbe van der WesthuizenNdeke MuseeMattheüs Theodor LootsNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-11 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Walter W. Focke Isbe van der Westhuizen Ndeke Musee Mattheüs Theodor Loots Kinetic interpretation of log-logistic dose-time response curves
description	Abstract A Hill-type time-response curve was derived using a single-step chemical kinetics approximation. The rate expression for the transformation is a differential equation that provides an interpolation formula between the logistic growth curve and second order kinetics. The solution is equivalent to the log-logistic cumulative distribution function with the time constant expressed in terms of a kinetic rate constant. This expression was extended to a full dose-time-response equation by postulating a concentration dependence for the rate constant. This was achieved by invoking a modified form of Haber’s law that connects an observed toxic effect with the concentration of the active agent and the elapsed exposure time. Analysis showed that the concept of Concentration Addition corresponds to a special case where the rate constant for the overall transformation rate is proportional to the sum of the rate constants that apply when the agents act individually. Biodiesel “survival” curves were measured and used to test the applicability of the empirical model to describe the effects of inhibitor dosage and binary inhibitor mixtures. Positive results suggest that the proposed dose-response relationship for the toxicity of agents to organisms can be extended to inanimate systems especially in cases where accurate mechanistic models are lacking.
format	article
author	Walter W. Focke Isbe van der Westhuizen Ndeke Musee Mattheüs Theodor Loots
author_facet	Walter W. Focke Isbe van der Westhuizen Ndeke Musee Mattheüs Theodor Loots
author_sort	Walter W. Focke
title	Kinetic interpretation of log-logistic dose-time response curves
title_short	Kinetic interpretation of log-logistic dose-time response curves
title_full	Kinetic interpretation of log-logistic dose-time response curves
title_fullStr	Kinetic interpretation of log-logistic dose-time response curves
title_full_unstemmed	Kinetic interpretation of log-logistic dose-time response curves
title_sort	kinetic interpretation of log-logistic dose-time response curves
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/5f95e45c60be4a42ab70ecd2253f8e8c
work_keys_str_mv	AT walterwfocke kineticinterpretationofloglogisticdosetimeresponsecurves AT isbevanderwesthuizen kineticinterpretationofloglogisticdosetimeresponsecurves AT ndekemusee kineticinterpretationofloglogisticdosetimeresponsecurves AT mattheustheodorloots kineticinterpretationofloglogisticdosetimeresponsecurves
_version_	1718394338090680320

Kinetic interpretation of log-logistic dose-time response curves

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