The original version of this article was published open access. Unfortunately, due to a technical issue, the copyright holder name in the online version (HTML and XML) is incorrectly published as ... Show moreThe original version of this article was published open access. Unfortunately, due to a technical issue, the copyright holder name in the online version (HTML and XML) is incorrectly published as "Springer Science+Business Media, LLC, part of Springer Nature 2018". Instead, it should be "The Author(s) 2018". Show less
Witte, W.E.A. de; Rottschäfer, V.; Danhof, M.; Graaf, P.H. van der; Peletier, L.A.; Lange, E.C.M. de 2018
In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase-planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear... Show moreIn this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase-planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor-pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not. Show less
Benson, N.; Graaf, P.H. van der; Peletier, L.A. 2016
A recently developed system-pharmacological model for the dynamics of receptor tyrosine kinases is used to compare di erent targets for drug action: one aiming at binding endogenous ligand needed... Show moreA recently developed system-pharmacological model for the dynamics of receptor tyrosine kinases is used to compare di erent targets for drug action: one aiming at binding endogenous ligand needed for phosphorylation and another binding re- ceptors at their kinase domains and thus preventing them to generate phosphory- lation. We obtain quantitative estimates for the e ectivity of the inhibitor which demonstrate the influence of drug-properties such as dose, a nity to target and drug-elimination rates. Show less
Graaf, P.H. van der; Benson, N.; Peletier, L.A. 2016
Mathematical analysis of pharmacological models is becoming increasingly rel- evant for drug development. Emphasis on mechanistic models has grown and qualitative understanding of complex... Show moreMathematical analysis of pharmacological models is becoming increasingly rel- evant for drug development. Emphasis on mechanistic models has grown and qualitative understanding of complex biological systems has improved a great deal. In this paper we present two examples of basic modular processes which are involved in a wide range of physiological systems. The first model concerns the interaction of a drug with its target, the way the compounds bind and then elicit an effect. The second model is central in signal trans- duction across the cell wall. Both models demonstrate the complex and interesting dynamics which is directly relevant for the impact of the drug. Show less
