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Direct, Indirect, and Signal Transduction Response Modeling

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Systems Pharmacology and Pharmacodynamics

Part of the book series: AAPS Advances in the Pharmaceutical Sciences Series ((AAPS,volume 23))

Abstract

Based on the paradigm of mechanistic modeling, three types of pharmacodynamic models are introduced: direct effect , indirect response , and signal transduction . The underlying pharmacological and biological assumptions about the model structures and operations are provided along with examples of their applications. A brief historical perspective is introduced for each model class. Mathematical equations defining the model are presented and explored to link model parameters with model characteristics such as the shape of the response curve. The impact of dose on the time courses of pharmacodynamic responses is evaluated for large doses and exemplified with computer simulations. A common theme is the extent of delay between drug pharmacokinetics and response. When relevant, alternative parameterization s and parameter identifiability are discussed. Only the simplest forms of models are provided with some guidelines on how to build more complex models based on a systems pharmacology approach.

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References

  • Ariens EJ (1954) Affinity and intrinsic activity in the theory of competitive inhibition. I. Problems and theory. Arch Int Pharmacodyn Ther 99:32–49

    CAS  PubMed  Google Scholar 

  • Bagli M, Süverkrüp R, Quadflieg R, Höflich G, Kasper S, Möller HJ, Langer M, Barlage U, Rao ML (1999) Pharmacokinetic-pharmacodynamic modeling of tolerance to the prolactin-secreting effect of chlorprothixene after different modes of drug administration. J Pharmacol Exp Ther 291:547–554

    CAS  PubMed  Google Scholar 

  • Black JW, Leff P (1983) Operational models of pharmacological agonism. Proc R Soc Lond B: Biol Sci 220:141–162

    Google Scholar 

  • Budha NR, Kovar A, Meibohm B (2011) Comparative performance of cell lifespan and cell transit models for describing erythropoietic drug effects. AAPS J 13:650–661

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bulitta JB, Zhao P, Arnold RD, Kessler DR, Daifuku R, Pratt J, Luciano G, Hanauske A-R, Gelderblom H, Awada A, Jusko WJ (2009) Multiple-pool cell lifespan models for neutropenia to assess the population pharmacodynamics of unbound paclitaxel from two formulations in cancer patients. Cancer Chemother Pharmacol 63:1035–1048

    Article  CAS  PubMed  Google Scholar 

  • Chakraborty A, Krzyzanski W, Jusko WJ (1999) Mathematical modeling of circadian cortisol concentrations using indirect response models: comparison of several methods. J Pharmacokinet Biopharm 27:23–43

    Article  CAS  PubMed  Google Scholar 

  • Clark AJ (1933) The mode of action of drugs on cells. Edward Arnold, London

    Google Scholar 

  • Davis PJ (1972) Gamma function and related functions. In: Abramowitz M, Stegun I (eds) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New York

    Google Scholar 

  • Detivaud L, Nemeth E, Boudjema K, Turlin B, Troadec MB, Leroyer P, Ropert M, Jacquelinet S, Courselaud B, Ganz T, Brissot P, Loreal O (2005) Hepcidin levels in humans are correlated with hepatic iron stores, hemoglobin levels, and hepatic function. Blood 106:746–748

    Article  CAS  PubMed  Google Scholar 

  • Dayneka NL, Garg V, Jusko WJ (1993) Comparison of four basic indirect pharmacodynamic responses. J Pharmacokinet Biopharm 21:457–478

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Dutta S, Matsumoto Y, Ebling WF (1996) Is it possible to estimate the parameters of the sigmoid Emax model with truncated data typical of clinical studies? J Pharm Sci 85:232–239

    Article  CAS  PubMed  Google Scholar 

  • Edeki T, Johnston A, Li Kam Wa E, Turner P (1994) Enalapril pharmacokinetics and ACE inhibition, following single and chronic oral dosing. Int J Clin Pharmacol Ther 32:142–146

    CAS  PubMed  Google Scholar 

  • Evans MA, Shanks CA, Brown KF, Triggs EJ (1984) Pharmacokinetic and pharmacodynamic modelling with pancuronium. Eur J Clin Pharmacol 26:243–250

    Article  CAS  PubMed  Google Scholar 

  • Frazier EP, Schneider T, Michel TM (2006) Effects of gender, age and hypertension on β-adrenergic receptor function in rat urinary bladder. Naunyn-Schmiedeberg’s Arch Pharmacol 373:300–309

    Article  CAS  Google Scholar 

  • Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO (2002) Model of chemotherapy induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20:4713–4721

    Article  PubMed  Google Scholar 

  • Furchgott RF (1966) The use of β-haloalkylamines in the differentiation of receptors and in the determination of dissociation constants receptor-agonist complexes. In: Harper NJ, Simmonds AB (eds) Adavnces in drug research, vol 3. Academic Press, New York

    Google Scholar 

  • Harker LA, Roskos LK, Marzec UM, Carter RA, Cherry JK, Sundell B, Cheung EL, Terry D, Sheridan W (2000) Effects of megakaryocyte growth and development factor on platelet production, platelet life span, and platelet function in healthy human volunteers. Blood 95:2514–2522

    CAS  PubMed  Google Scholar 

  • Hazra A, Krzyzanski, Jusko WJ (2006) Mathematical assessment of properties of precursor-dependent indirect pharmacodynamic response models. J Pharmacokin Pharmacodyn 33:683–717

    Article  CAS  Google Scholar 

  • Hill A (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40:IV–VIII

    Google Scholar 

  • Jamal NM, Krzyzanski W, Cheung W, Lau CY, Messner HA (2006) Evaluation of epoetin alpha (rHuEPO) and darbepoetin alpha (DARB) on human burst-colony formation (BFU-E) in culture. J Int Med Res 34:42–51

    Article  CAS  PubMed  Google Scholar 

  • Jordan P, Gieschke R (2005) Explicit solutions for a class of indirect pharmacodynamic response models. Comput Methods Programs Biomed 77:91–97

    Article  CAS  PubMed  Google Scholar 

  • Jusko WJ (2013) Moving from basic toward systems pharmacodynamic models. J Pharm Sci 102:2930–2940

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Jusko WJ, Ko HC (1994) Physiologic indirect response models characterize diverse types of pharmacodynamic effects. Clin Pharmacol Ther 56:406–419

    Article  CAS  PubMed  Google Scholar 

  • Jusko WJ, Ko HC, Ebling WF (1995) Convergence of direct and indirect pharmacodynamic response models. J Pharmacokinet Biopharm 23:5–8

    Article  CAS  PubMed  Google Scholar 

  • Kenakin TP (2006) A pharmacology primer. Theory, applications, and methods. Elsevier, Amsterdam

    Google Scholar 

  • Koch G, Schropp J (2013) Solution and implementation of distributed lifespan models. J Pharmacokinet Pharmacodyn 40(6):639–650

    Article  PubMed  Google Scholar 

  • Krzyzanski W, Dmochowski J, Matsushima N, Jusko WJ (2006) Assessment of dosing impact on intra-individual variability in estimation of parameters for basic indirect response models. J Pharmacokin Pharmacodyn 33:635–655

    Article  Google Scholar 

  • Krzyzanski W, Jusko WJ (1997) Mathematical formalism for the properties of four basic models of indirect pharmacodynamic responses. J Pharmacokin Biopharm 25:107–123

    Article  CAS  Google Scholar 

  • Krzyzanski W, Jusko WJ (1998) Characterization of pharmacodynamic recession slopes for direct and indirect response models. J Pharmacokin Biopharm 26:409–436

    Article  CAS  Google Scholar 

  • Krzyzanski W, Perez Ruixo JJ (2012) Lifespan based indirect response modelds. J Pharmacokinet Pharmacodyn 39:109–123

    Article  PubMed  PubMed Central  Google Scholar 

  • Krzyzanski W, Ramakrishnan R, Jusko WJ (1999) Basic models for agents that alter production of natural cells. J Pharmacokin Biopharm 27:467–489

    Article  CAS  Google Scholar 

  • Labrecque G, Belanger PM (1991) Biological rhythms in the absorption, distribution, metabolism and excretion of drugs. Pharmacol Ther 52:95–107

    Article  CAS  PubMed  Google Scholar 

  • Levy G (1966) Kinetics of pharmacologic effects. Clin Pharmacol Ther 7:362–372

    Article  CAS  PubMed  Google Scholar 

  • Lew KH, Ludwig EA, Milad MA, Donovan K, Middleton E Jr, Ferry JJ, Jusko WJ (1993) Gender-based effects on methylprednisolone pharmacokinetics and pharmacodynamics. Clin Pharmacol Ther 54:402–414

    Google Scholar 

  • Nagashima R, O’Reilly RA, Levy G (1969) Kinetics of pharmacologic effects, in man: the anticoagulant action of warfarin. Clin Pharmacol Ther 10:22–35

    Article  CAS  PubMed  Google Scholar 

  • Magee MH, Blum RA, Lates CD, Jusko WJ (2001) Prednisolone pharmacokinetics and pharmacodynamics in relation to sex and race. J Clin Pharmacol 41:1180–1194

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Mager DE, Jusko WJ (2001) Pharmacodynamic modeling of time-dependent transduction systems. Clin Pharmacol Ther 70:210–216

    Google Scholar 

  • Mager DE, Wyska E, Jusko WJ (2003) Diversity of mechanism-based pharmacodynamic models. Drug Met Disp 31:510–518

    Article  CAS  Google Scholar 

  • Mo G, Gibbons F, Schroeder P, Krzyzanski W (2014) Lifespan based pharmacokinetic-pharmacodynamic model of tumor growth inhibition by anticancer therapeutics. PLoS ONE 9(10):e109747

    Google Scholar 

  • Peletier LA, Gabrielsson J, den Haag J (2005) A dynamical systems analysis of the indirect response model with special emphasis on time to peak response. J Pharmacokinet Pharmacodyn 32:607–654

    Article  PubMed  Google Scholar 

  • Peng JZ, Denney WS, Musser BJ, Liu R, Tsai K, Fang L, Reitman ML, Troyer MD, Engel SS, Xu L, Stoch A, Stone JA, Kowalski KG (2014) A semi-mechanistic model for the effects of a novel glucagon receptor antagonist on glucagon and the interaction between glucose, glucagon, and insulin applied to adaptive phase II design. AAPS J 16:1259–1270

    Google Scholar 

  • Perlstein I, Stepansky D, Krzyzanski W, Hofman A (2002) A signal transduction pharmacodynamic model of the kinetics of parasympathomimetic activity of low-dose scopolamine and atropine in rats. J Pharm Sci 91:2500–2510

    Article  CAS  PubMed  Google Scholar 

  • Ramakrishnan R, DuBois D, Almon RA, Pyszczynski NA, Jusko WJ (2002) Fifth-generation model for corticosteroid pharmacodynamics: steady-state receptor down-regulation and enzyme induction patterns during seven-day continuous infusion of methylprednisolone in rats. J Pharmacokin Pharmacodyn 29:1–24

    Article  CAS  Google Scholar 

  • Reppert SM, Weaver DR (2002) Coordination of circadian timing in mammals. Nature 418:935–941

    Article  CAS  PubMed  Google Scholar 

  • Rohatagi S, Bye A, Falcoz C, Mackie AE, Meibohm B, Mollmann H, Derendorf H (1996) Dynamic modeling of cortisol reduction after inhaled administration of fluticasone proprionate. J Clin Pharmacol 36:938–941

    Article  CAS  PubMed  Google Scholar 

  • Sallstrom B, Visser SAG, Forsberg T, Peletier LA, Ericson AC, Gabrielsson J (2005) A pharmacodynamics turnover model capturing assymetric circadian baselines of body temperature, heart rate and blood pressure in rats: challenges in terms of tolerance and animal-handling effects. J Pharmacokinet Pharmacodyn 32:835–859

    Article  PubMed  Google Scholar 

  • Samtani MN, Perez-Ruixo JJ, Brown K, Carneus D, Molloy C (2009) Pharmacokinetic and pharmacodynamic modeling of pegylated thrombopoietin mimetic peptide (PEG0TPOm) after single intravenous dose in healthy subjects. J Clin Pharmacol 49:336–350

    Article  CAS  PubMed  Google Scholar 

  • Savic RM, Jonker DM, Kerbusch T, Karlsson MO (2007) Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies. J Pharmacokinet Pharmacodyn 34:711–726

    Article  CAS  PubMed  Google Scholar 

  • Schwartz JB, Verotta D, Sheiner LB (1989) Pharmacodynamic modeling of verapamil effects under steady-state and nonsteady state conditions. J Pharmacol Exp Ther 251:1032–1038

    CAS  PubMed  Google Scholar 

  • Sharma A, Ebling WF, Jusko WJ (1998) Precursor-dependent indirect pharmacodynamic response model for tolerance and rebound phenomena. J Pharm Sci 87:1577–1584

    Article  CAS  PubMed  Google Scholar 

  • Sharma A, Jusko WJ (1996) Characterization of four basic models of indirect pharmacodynamics responses. J Pharmacokin Biopharm 24:611–635

    Article  CAS  Google Scholar 

  • Sheiner LB, Stansky DR, Vozeh S, Miller RD, Ham J (1979) Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharmacol Ther 25:358–371

    Article  CAS  PubMed  Google Scholar 

  • Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, Germani M, Poggesi I, Rocchetti M (2004) Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res 64:1094–1101

    Article  CAS  PubMed  Google Scholar 

  • Stephenson RP (1956) A modification of receptor theory. Br J Pharmacol 11:379–393

    CAS  Google Scholar 

  • Sukumaran S, Almon RR, DuBois DC, Jusko WJ (2010) Circadian rhythms in gene expression: Relationship to physiology, disease, drug disposition and drug action. Adv Drug Deliv Rev 62:904–917

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Sun YN, Jusko WJ (1998) Transit compartments versus gamma distribution function to model signal transduction processes in pharmacodynamics. J Pharm Sci 87:732–737

    Article  CAS  PubMed  Google Scholar 

  • Van der Graaf PH, Van Schaick EA, Matho RAA, Ijzermn AP, Danhof M (1997) Mechanism-based pharmacokinetic-pharmacodynamic modeling of the effects of N6-cyclopentyladenosine analogs on heart rate in rat: Estimation of in vivo operational affinity and efficacy at adenosine A1 receptors. J Pharmacol Exp Ther 283:809–816

    Google Scholar 

  • Wagner JG (1968) Kinetics of pharmacologic response: I. Proposed relationship between response and drug concentration in the intact animal and man. J Theor Biol 20:173–201

    Article  CAS  PubMed  Google Scholar 

  • Whiting B, Kelman AW, Barclay J, Addis GJ (1981) Modeling theophylline response in individual patients with chronic bronchitis. Br J Clin Pharmacol 12:481

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Yamakage M (1992) Direct inhibitory mechanism of halothane on canine tracheal smooth muscle contraction. Anesthesiology 77:546–553

    Article  CAS  PubMed  Google Scholar 

  • Yao Z, Krzyzanski W, Jusko WJ (2006) Assessment of basic indirect pharmacodynamic response models with physiological limits. J Pharmacokin Pharmacodyn 33:167–193

    Google Scholar 

  • Yates JWT (2008) Mathematical properties and parameter estimation for transit compartment pharmacodynamic models. Eur J Pharm Sci 34:104–109

    Article  CAS  PubMed  Google Scholar 

  • Zelen M, Severo NC (1972) Probability functions. In: Abramowitz M, Stegun IA (eds) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New York

    Google Scholar 

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Authors and Affiliations

  1. Department of Pharmaceutical Sciences, University at Buffalo, SUNY, 370 Kapoor Hall, Buffalo, NY, 14214, USA

    Wojciech Krzyzanski

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  1. Wojciech Krzyzanski
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Correspondence to Wojciech Krzyzanski .

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Editors and Affiliations

  1. Department of Pharmaceutical Sciences, University at Buffalo, SUNY, Buffalo, New York, USA

    Donald E. Mager

  2. Global Clinical Pharmacology, Janssen Research and Development, LLC,, Spring House, Pennsylvania, USA

    Holly H.C. Kimko

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Krzyzanski, W. (2016). Direct, Indirect, and Signal Transduction Response Modeling. In: Mager, D., Kimko, H. (eds) Systems Pharmacology and Pharmacodynamics. AAPS Advances in the Pharmaceutical Sciences Series, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-44534-2_9

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