A Dynamical Systems Analysis of the Indirect Response Model with Special Emphasis on Time to Peak Response

Peletier, L. A.; Gabrielsson, Johan; Haag, Jacintha den

doi:10.1007/s10928-005-0047-x

Cited by 22 publications

(12 citation statements)

References 20 publications

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“…Differentiating this identity with respect to D we obtain an expression for T (D) similar to (11). We find that if ακ 1, the integral on the right of this expression can be shown to be positive for all drug doses.…”

Section: Sketch Of the Proof Of Theorem 11mentioning

confidence: 84%

“…Their mathematical properties have also been actively studied (cf. [12,[4][5][6]8,11]). Following Dayneka, Garg and Jusko [2], we number these models I, II, III and IV, as explained in the schematic picture shown in Fig.…”

Section: H (C) = S(c)) or Inhibiting (H (C) = I (C)) In This Paper Tmentioning

confidence: 99%

“…[11]), it suffices to prove monotonicity for one of them; we do it for Model III. Thus, we consider the problem:…”

Section: Sketch Of the Proof Of Theorem 11mentioning

confidence: 99%

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Monotonicity of the peak time in turnover models

Nguyên

Peletier

2009

Comptes Rendus. Mathématique

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We prove that in three of the classical turnover models in pharmacodynamics the time to maximal response increases with increasing drug dose when the concentration of the drug in the blood plasma decreases exponentially with time. Version française abrégéeDans cette Note, nous présentons des résultats récents sur la façon dont le Temps de Réponse Maximal dépend de la dose de drogue dans des systèmes décrits par les quatre modèles turnovers classiques en pharmacodynamique (voir, par exemple, [1,9,2]). Dans des modèles turnovers, la réponse R est décrite par une équation différentielle ordinaire linéaire du premier ordre :où k in et k out sont constantes. Ici C(t) est la concentration du médicament dans le plasma, H 1 et H 2 sont fonctions qui décrivent l'effet de la dose de drogue D. Elles peuvent être stimulantes (H (C) = S(C)) ou inhibitrices (H (C) = I (C)). Dans cette Note, les fonctions S, I , et C sont données par :

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Section: Sketch Of the Proof Of Theorem 11mentioning

confidence: 84%

Section: H (C) = S(c)) or Inhibiting (H (C) = I (C)) In This Paper Tmentioning

confidence: 99%

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Monotonicity of the peak time in turnover models

Nguyên

Peletier

2009

Comptes Rendus. Mathématique

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“…This greater than additive (i.e., synergistic) action when compounds are combined can be explained by their cooperative effect originating from simultaneous stimulation of production of response and inhibition of its loss. Also, a faster return of the response back to baseline with the combination treatment may be indicative either of rapid tolerance development or the early cessation of inhibitory action by agent A on factors determining the loss of response (20).…”

Section: Case Studymentioning

confidence: 99%

Pattern Recognition in Pharmacodynamic Data Analysis

Gabrielsson

Stephan

2015

AAPS J

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Abstract. Pattern recognition is a key element in pharmacodynamic analyses as a first step to identify drug action and selection of a pharmacodynamic model. The essence of this process is going from data to insight through exploratory data analysis. There are few formal strategies that scientists typically use when the experiment has been done and data collected. This report attempts to ameliorate this deficit by identifying the properties of a pharmacodynamic model via dissection of the pattern revealed in responsetime data. Pattern recognition in pharmacodynamic analyses contrasts with pharmacokinetic analyses with respect to time course. Thus, the time course of drug in plasma usually differs markedly from the time course of the biomarker response, as a consequence of a myriad of interactions (transport to biophase, binding to target, activation of target and downstream mediators, physiological response, cascade and amplification of biosignals, homeostatic feedback) between the events of exposure to test compound and the occurrence of the biomarker response. Homing in on this important-but less often addressed-element, 20 datasets of varying complexity were analyzed, and from this, we summarize a set of points to consider, specifically addressing baseline behavior, number of phases in the response-time course, time delays between concentration-and response-time courses, peak shifts in response with increasing doses, saturation, and other potential nonlinearities. These strategies will hopefully give a better understanding of the complete pharmacodynamic response-time profile.

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“…The transient and switch-like induction of the system by the applied pulsed stimuli is abstracted to a general switching function to allow analyses of different input kinetics. This common network structure closely resembles response models such as turn-over models from the field of pharmacodynamics (Dayneka et al 1993;Krzyzanski and Jusko 1997;Peletier et al 2005), which have been used to study the properties of time-to peak responses (Gabrielsson and Weiner 1997;Mager et al 2003). Therefore, we base our work on these turnover models, but extend them to allow for arbitrary drug decays, which corresponds to the switching function in the discussed ligand-receptor kinetics.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of Time-to-Peak Responses in Biological Reaction Networks

Theis

Böhl²,

Klingmüller³

2010

Bull Math Biol

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Processing of information by signaling networks is characterized by properties of the induced kinetics of the activated pathway components. The maximal extent of pathway activation (maximum amplitude) and the time-to-peak-response (position) are key determinants of biological responses that have been linked to specific outcomes. We investigate how the maximum amplitude of pathway activation and its position depend on the input and wiring of a signaling network. For this purpose, we consider a simple reaction A→B that is regulated by a transient input and extended this to include back-reaction and additional partners. In particular, we show that a unique maximum of B(t) exists. Moreover, we prove that the position of the maximum is independent of the applied input but regulated by degradation reactions of B. Indeed, the time-to-peak-response decreases with increasing degradation rate, which we prove for small models and show in simulations for more complex ones. The identified dependencies provide insights into design principles that facilitate the realization dynamical characteristics like constant position of maximal pathway activation and thereby guide the characterization of unknown kinetics within larger protein networks.

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A Dynamical Systems Analysis of the Indirect Response Model with Special Emphasis on Time to Peak Response

Cited by 22 publications

References 20 publications

Monotonicity of the peak time in turnover models

Monotonicity of the peak time in turnover models

Pattern Recognition in Pharmacodynamic Data Analysis

Theoretical Analysis of Time-to-Peak Responses in Biological Reaction Networks

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