Dynamics of a two-receptor binding model: How affinities and capacities translate into long and short time behaviour and physiological corollaries

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September 2012, 17(6): 2171-2184. doi: 10.3934/dcdsb.2012.17.2171

Dynamics of a two-receptor binding model: How affinities and capacities translate into long and short time behaviour and physiological corollaries

Lambertus A. Peletier ^1, , Willem de Winter ^2, and An Vermeulen ^2,

1.	Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, Netherlands
2.	Advanced Modeling & Simulation; Clinical Pharmacology, Janssen Research & Development, a division of Janssen Pharmaceutica N.V., Turnhoutseweg 30, 2340 Beerse, Belgium, Belgium

Received July 2011 Revised February 2012 Published May 2012

Abstract
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In this paper we present a mathematical analysis of a model involving target-mediated drug disposition involving two targets, developed to fit a series of data sets. The two targets are receptors with very different characteristics: one has high affinity to the drug, a small capacity and a short half-life, whilst the other receptor has low affinity to the drug, high capacity and its half-life is large. The analysis of this model yields a qualitative and quantitative understanding of the dynamics of this two-receptor model and in particular identifies different time scales over which the amounts of free drug and drug-receptor complexes vary. Thus it yields analytical tools to make long-term predictions on the basis of medium term data sets.

Keywords: singular perturbation theory., protein binding, Target-mediated drug disposition, systems pharmacology.

Mathematics Subject Classification: Primary: 34C20, 34D15; Secondary: 92C42, 92C45, 80A3.

Citation: Lambertus A. Peletier, Willem de Winter, An Vermeulen. Dynamics of a two-receptor binding model: How affinities and capacities translate into long and short time behaviour and physiological corollaries. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 2171-2184. doi: 10.3934/dcdsb.2012.17.2171

References:

[1]	L. Gibiansky, E. Gibiansky, T. Kakkar and P. Ma, Approximations of the target-mediated drug disposition model and identifying of model parameters, J. Pharmacokinetics Phamacodynamics, 35 (2008), 573-591. doi: 10.1007/s10928-008-9102-8.
[2]	L. Gibiansky and E. Gibiansky, Target-mediated drug disposition model for drugs that bind to more than one target, J. Pharmacokinetics Phamacodynamics, 37 (2010), 323-346. doi: 10.1007/s10928-010-9163-3.
[3]	D. Mager and W. J. Jusko, General pharmacokinetic model for drugs exhibiting target-mediated drug disposition, J. Pharmacokinetics and Phamacodynamics, 28 (2001), 507-532. doi: 10.1023/A:1014414520282.
[4]	D. Mager and W. Krzyzanski, Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition, Pharm. Research, 22 (2005), 1589-1596. doi: 10.1007/s11095-005-6650-0.
[5]	L. Michaelis and M. L. Menten, Die Kinetik der Invertinwirkung, Biochem. Z., 49 (1913), 333-369.
[6]	L. A. Peletier and J. Gabrielsson, Dynamics of target-mediated drug disposition, European Journal of Pharmaceutical Sciences, 38 (2009), 445-464. doi: 10.1016/j.ejps.2009.09.007.
[7]	L. A. Peletier, N. Benson and P. H. van der Graaf, Impact of plasma-protein binding on receptor occupancy: An analytical description, J. Theor. Biology, 256 (2009), 253-262. doi: 10.1016/j.jtbi.2008.09.014.
[8]	E. Snoeck, Ph. Jacqmin, A. van Peer and M. Danhof, A combined specific target site binding and pharmacokinetic model to explore the non-linear disposition of draflazine, J. Pharmacokinetics and Biopharmaceutics, 27 (1999), 257-281. doi: 10.1023/A:1020943029130.
[9]	L. A. Segel, On the validity of the steady state assumption of enzyme kinetics, Bull. Math. Biol., 50 (1988), 579-593. doi: 10.1016/S0092-8240(88)80057-0.
[10]	L. A. Segel and M. Slemrod, The quasi-steady state assumption: A case study in perturbation, SIAM Review, 31 (1989), 446-477. doi: 10.1137/1031091.
[11]	Y. Sugiyama and M. Hanano, Receptor-mediated transport of peptide hormones and its importance in the overall hormone disposition in the body, Pharm. Research 6 (1989), 192-202.

show all references

References:

[1]	L. Gibiansky, E. Gibiansky, T. Kakkar and P. Ma, Approximations of the target-mediated drug disposition model and identifying of model parameters, J. Pharmacokinetics Phamacodynamics, 35 (2008), 573-591. doi: 10.1007/s10928-008-9102-8.
[2]	L. Gibiansky and E. Gibiansky, Target-mediated drug disposition model for drugs that bind to more than one target, J. Pharmacokinetics Phamacodynamics, 37 (2010), 323-346. doi: 10.1007/s10928-010-9163-3.
[3]	D. Mager and W. J. Jusko, General pharmacokinetic model for drugs exhibiting target-mediated drug disposition, J. Pharmacokinetics and Phamacodynamics, 28 (2001), 507-532. doi: 10.1023/A:1014414520282.
[4]	D. Mager and W. Krzyzanski, Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition, Pharm. Research, 22 (2005), 1589-1596. doi: 10.1007/s11095-005-6650-0.
[5]	L. Michaelis and M. L. Menten, Die Kinetik der Invertinwirkung, Biochem. Z., 49 (1913), 333-369.
[6]	L. A. Peletier and J. Gabrielsson, Dynamics of target-mediated drug disposition, European Journal of Pharmaceutical Sciences, 38 (2009), 445-464. doi: 10.1016/j.ejps.2009.09.007.
[7]	L. A. Peletier, N. Benson and P. H. van der Graaf, Impact of plasma-protein binding on receptor occupancy: An analytical description, J. Theor. Biology, 256 (2009), 253-262. doi: 10.1016/j.jtbi.2008.09.014.
[8]	E. Snoeck, Ph. Jacqmin, A. van Peer and M. Danhof, A combined specific target site binding and pharmacokinetic model to explore the non-linear disposition of draflazine, J. Pharmacokinetics and Biopharmaceutics, 27 (1999), 257-281. doi: 10.1023/A:1020943029130.
[9]	L. A. Segel, On the validity of the steady state assumption of enzyme kinetics, Bull. Math. Biol., 50 (1988), 579-593. doi: 10.1016/S0092-8240(88)80057-0.
[10]	L. A. Segel and M. Slemrod, The quasi-steady state assumption: A case study in perturbation, SIAM Review, 31 (1989), 446-477. doi: 10.1137/1031091.
[11]	Y. Sugiyama and M. Hanano, Receptor-mediated transport of peptide hormones and its importance in the overall hormone disposition in the body, Pharm. Research 6 (1989), 192-202.

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