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Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency.

Aston, PJ, Derks, G, Raji, A, Agoram, BM and van der Graaf, PH (2011) Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency. J Theor Biol, 281 (1). 113 - 121. ISSN 0022-5193

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Abstract

We consider the relationship between the target affinity of a monoclonal antibody and its in vivo potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment. From the differential equations, we derive two expressions for this minimum level in terms of the parameters of the problem, one of which is valid over the full range of values of the equilibrium dissociation constant K(D) and the other which is valid only for a large drug dose or for a small value of K(D). Both of these formulae show that the potency achieved by increasing the association constant k(on) can be very different from the potency achieved by decreasing the dissociation constant k(off). In particular, there is a saturation effect when decreasing k(off) where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing k(on). Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing k(on) than by decreasing k(off).

Item Type: Article
Additional Information: NOTICE: this is the submitted version (pre-print) of a work that was subsequently accepted for publication in Journal of Theoretical Biology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Journal of Theoretical Biology 281 (1) 2011 DOI 10.1016/j.jtbi.2011.04.030
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 30 Nov 2012 10:11
Last Modified: 23 Sep 2013 18:55
URI: http://epubs.surrey.ac.uk/id/eprint/39605

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