Modeling drug-protein dynamics

Previous Article
Stability of the steady state for multi-dimensional thermoelastic systems of shape memory alloys
DCDS-S Home
This Issue
Next Article
Stripe patterns and the Eikonal equation

February 2012, 5(1): 191-207. doi: 10.3934/dcdss.2012.5.191

Modeling drug-protein dynamics

Lambertus A. Peletier ^1,

1.	Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, Netherlands

Received March 2009 Revised January 2010 Published February 2011

Abstract
Related Papers

In this paper we discuss two models involving protein binding. The first model describes a system involving a drug, a receptor and a protein, and the question is to what extent the affinity of the drug to the protein affects the drug-receptor binding and thereby the efficiency of the drug. The second model is the basic model underlying Target-Mediated Drug Disposition, which describes the pharmacokinetics of a drug in the presence of a target, often a receptor.

Keywords: singular perturbation theory, target-mediated drug disposition, systems biology., Michaelis-Menten, Protein binding, pharmacokinetics.

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

Citation: Lambertus A. Peletier. Modeling drug-protein dynamics. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 191-207. doi: 10.3934/dcdss.2012.5.191

References:

[1]	D. J. A. Crommelin (ed), Robert D. Sindelar (ed) and Bernd Meibohm (ed), "Pharmaceutical Biotechnology: Fundamentals and Applications," Informa Healthcare, 2008.
[2]	L. Gibiansky, E. Gibiansky, T. Kakkar and P. Ma, Approximations of the target-mediated drug disposition model and identifiability of model parameters, J. Pharmacokinet. Phamacodyn., 35 (2008), 573-591. doi: 10.1007/s10928-008-9102-8.
[3]	T. Kenakin, "A Pharmacology Primer: Theory, Application and Methods," Elsevier Academic Press, 2004.
[4]	B.-F. Krippendorff, K. Kuester, C. Kloft and W. Huisinga, Nonlinear pharmacokinetics and therapeutic proteins resulting from receptor-mediated endocytosis, J. Pharmacokinet. Phamacodyn., 36 (2009,) 239-260.
[5]	G. Levy, Pharmacologic target mediated drug disposition, Clin. Pharmacol. Ther., 56 (1994), 248-252. doi: 10.1038/clpt.1994.134.
[6]	D. E. Mager, Target-mediated drug disposition and dynamics, Biochem. Pharmacology, 72 (2006), 1-10. doi: 10.1016/j.bcp.2005.12.041.
[7]	D. E. Mager and W. J. Jusko, General pharmacokinetic model for drugs exhibiting target-mediated drug disposition, J. Pharmacokinet. Phamacodyn., 28 (2001), 507-532. doi: 10.1023/A:1014414520282.
[8]	D. E. 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.
[9]	B. K. Martin, Kinetics of elimination of drugs possessing high affinity for the plasma proteins, Nature, 207 (1965), 959-960. doi: 10.1038/207959a0.
[10]	B. Meibohm (ed), "Pharmacokinetics and Pharmacodynamics of Biotech Drugs: Principles and Case Studies in Drug Development," Wiley-VCH Verlag GmbH & Co KGaA, Weinheim, Germany, 2006.
[11]	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.
[12]	L. A. Peletier and J. Gabrielsson, Dynamics of target-mediated drug disposition, Eur. J. of Pharm. Sci., 38 (2009), 445-464. doi: 10.1016/j.ejps.2009.09.007.
[13]	R. L. Rich, Y. S. Day, T. A. Morton, D. G. Myszka, High-resolution and high-throughput protocols for measuring drug/Human Serum Albumin interactions using BIACORE, Anal. Biochem., 296 (2001), 197-207. doi: 10.1006/abio.2001.5314.
[14]	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. doi: 10.1023/A:1015905331391.
[15]	G. L. Trainor, The importance of plasma protein binding in drug discovery, Expert Opin. Drug. Discov., 2 (2007), 51-64. doi: 10.1517/17460441.2.1.51.
[16]	J. G. Wagner, A new generalised nonlinear pharmacokinetic model and its implications, in J. G. Wagner (ed), Biopharmaceutics and relevant pharmacokinetics, Drug Intelligence Publications, Hamilton, pp. 302-317, (1971).

show all references

References:

[1]	D. J. A. Crommelin (ed), Robert D. Sindelar (ed) and Bernd Meibohm (ed), "Pharmaceutical Biotechnology: Fundamentals and Applications," Informa Healthcare, 2008.
[2]	L. Gibiansky, E. Gibiansky, T. Kakkar and P. Ma, Approximations of the target-mediated drug disposition model and identifiability of model parameters, J. Pharmacokinet. Phamacodyn., 35 (2008), 573-591. doi: 10.1007/s10928-008-9102-8.
[3]	T. Kenakin, "A Pharmacology Primer: Theory, Application and Methods," Elsevier Academic Press, 2004.
[4]	B.-F. Krippendorff, K. Kuester, C. Kloft and W. Huisinga, Nonlinear pharmacokinetics and therapeutic proteins resulting from receptor-mediated endocytosis, J. Pharmacokinet. Phamacodyn., 36 (2009,) 239-260.
[5]	G. Levy, Pharmacologic target mediated drug disposition, Clin. Pharmacol. Ther., 56 (1994), 248-252. doi: 10.1038/clpt.1994.134.
[6]	D. E. Mager, Target-mediated drug disposition and dynamics, Biochem. Pharmacology, 72 (2006), 1-10. doi: 10.1016/j.bcp.2005.12.041.
[7]	D. E. Mager and W. J. Jusko, General pharmacokinetic model for drugs exhibiting target-mediated drug disposition, J. Pharmacokinet. Phamacodyn., 28 (2001), 507-532. doi: 10.1023/A:1014414520282.
[8]	D. E. 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.
[9]	B. K. Martin, Kinetics of elimination of drugs possessing high affinity for the plasma proteins, Nature, 207 (1965), 959-960. doi: 10.1038/207959a0.
[10]	B. Meibohm (ed), "Pharmacokinetics and Pharmacodynamics of Biotech Drugs: Principles and Case Studies in Drug Development," Wiley-VCH Verlag GmbH & Co KGaA, Weinheim, Germany, 2006.
[11]	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.
[12]	L. A. Peletier and J. Gabrielsson, Dynamics of target-mediated drug disposition, Eur. J. of Pharm. Sci., 38 (2009), 445-464. doi: 10.1016/j.ejps.2009.09.007.
[13]	R. L. Rich, Y. S. Day, T. A. Morton, D. G. Myszka, High-resolution and high-throughput protocols for measuring drug/Human Serum Albumin interactions using BIACORE, Anal. Biochem., 296 (2001), 197-207. doi: 10.1006/abio.2001.5314.
[14]	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. doi: 10.1023/A:1015905331391.
[15]	G. L. Trainor, The importance of plasma protein binding in drug discovery, Expert Opin. Drug. Discov., 2 (2007), 51-64. doi: 10.1517/17460441.2.1.51.
[16]	J. G. Wagner, A new generalised nonlinear pharmacokinetic model and its implications, in J. G. Wagner (ed), Biopharmaceutics and relevant pharmacokinetics, Drug Intelligence Publications, Hamilton, pp. 302-317, (1971).

[1]	Urszula Ledzewicz, Helen Moore. Optimal control applied to a generalized Michaelis-Menten model of CML therapy. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 331-346. doi: 10.3934/dcdsb.2018022
[2]	Jagadeesh R. Sonnad, Chetan T. Goudar. Solution of the Michaelis-Menten equation using the decomposition method. Mathematical Biosciences & Engineering, 2009, 6 (1) : 173-188. doi: 10.3934/mbe.2009.6.173
[3]	Maciej Leszczyński, Urszula Ledzewicz, Heinz Schättler. Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2315-2334. doi: 10.3934/dcdsb.2019097
[4]	Karl Peter Hadeler. Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1541-1560. doi: 10.3934/mbe.2013.10.1541
[5]	Ming Liu, Dongpo Hu, Fanwei Meng. Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. Discrete and Continuous Dynamical Systems - S, 2021, 14 (9) : 3197-3222. doi: 10.3934/dcdss.2020259
[6]	Rebeccah E. Marsh, Jack A. Tuszyński, Michael Sawyer, Kenneth J. E. Vos. A model of competing saturable kinetic processes with application to the pharmacokinetics of the anticancer drug paclitaxel. Mathematical Biosciences & Engineering, 2011, 8 (2) : 325-354. doi: 10.3934/mbe.2011.8.325
[7]	Fabio Camilli, Annalisa Cesaroni. A note on singular perturbation problems via Aubry-Mather theory. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 807-819. doi: 10.3934/dcds.2007.17.807
[8]	Manfred Deistler. Singular arma systems: A structure theory. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 383-391. doi: 10.3934/naco.2019025
[9]	Jeng-Huei Chen. An analysis of functional curability on HIV infection models with Michaelis-Menten-type immune response and its generalization. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2089-2120. doi: 10.3934/dcdsb.2017086
[10]	Eugene Kashdan, Dominique Duncan, Andrew Parnell, Heinz Schättler. Mathematical methods in systems biology. Mathematical Biosciences & Engineering, 2016, 13 (6) : i-ii. doi: 10.3934/mbe.201606i
[11]	Chris Guiver. The generalised singular perturbation approximation for bounded real and positive real control systems. Mathematical Control and Related Fields, 2019, 9 (2) : 313-350. doi: 10.3934/mcrf.2019016
[12]	Nathan Glatt-Holtz, Mohammed Ziane. Singular perturbation systems with stochastic forcing and the renormalization group method. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1241-1268. doi: 10.3934/dcds.2010.26.1241
[13]	Tuoi Vo, William Lee, Adam Peddle, Martin Meere. Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅰ: Drug transport. Mathematical Biosciences & Engineering, 2017, 14 (2) : 491-509. doi: 10.3934/mbe.2017030
[14]	Stéphane Chrétien, Sébastien Darses, Christophe Guyeux, Paul Clarkson. On the pinning controllability of complex networks using perturbation theory of extreme singular values. application to synchronisation in power grids. Numerical Algebra, Control and Optimization, 2017, 7 (3) : 289-299. doi: 10.3934/naco.2017019
[15]	D. Warren, K Najarian. Learning theory applied to Sigmoid network classification of protein biological function using primary protein structure. Conference Publications, 2003, 2003 (Special) : 898-904. doi: 10.3934/proc.2003.2003.898
[16]	Adam Peddle, William Lee, Tuoi Vo. Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅱ: Cell proliferation. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1117-1135. doi: 10.3934/mbe.2018050
[17]	Eduard Marušić-Paloka, Igor Pažanin. Homogenization and singular perturbation in porous media. Communications on Pure and Applied Analysis, 2021, 20 (2) : 533-545. doi: 10.3934/cpaa.2020279
[18]	Monique Chyba, Benedetto Piccoli. Special issue on mathematical methods in systems biology. Networks and Heterogeneous Media, 2019, 14 (1) : i-ii. doi: 10.3934/nhm.20191i
[19]	John Boyd. Strongly nonlinear perturbation theory for solitary waves and bions. Evolution Equations and Control Theory, 2019, 8 (1) : 1-29. doi: 10.3934/eect.2019001
[20]	Ilona Gucwa, Peter Szmolyan. Geometric singular perturbation analysis of an autocatalator model. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 783-806. doi: 10.3934/dcdss.2009.2.783

2021 Impact Factor: 1.865

Tools

Metrics

Other articles
by authors

on AIMS
Lambertus A. Peletier
on Google Scholar
Lambertus A. Peletier

[Back to Top]