Bulletin of Mathematical Biology

, Volume 81, Issue 9, pp 3642–3654 | Cite as

An Invitation to Pharmacostatics

  • Gilles GnacadjaEmail author
Special Issue: Mathematics to Support Drug Discovery and Development


Pharmacology, the study of interactions between biological processes and therapeutic agents, is traditionally presented as consisting of two subdisciplines: pharmacokinetics, which is about the distribution and metabolism of drugs in organisms, and pharmacodynamics, which is about the organisms’ response to drugs. In discovery-stage pharmacology however, one primary concern is what we call pharmacostatics, the characterization of equilibrium parameters and states of core interactions of physiologic and therapeutic interest. This usually takes the form of studying dose-response curves, without consideration for the relevant qualitative properties of the underlying reaction networks, e.g., the existence, multiplicity and asymptotic stability of steady states. Furthermore, steady-state calculations customarily employ manually derived closed-form expressions based on approximating assumptions. While these formulas may seem adequate most of the time, the assumptions need not apply, and there are genuine though seemingly uncommon cases where this approach is not feasible and/or fails to explain non-monotone dose-response curves. It is this paper’s aim to stimulate interest in mathematical problems arising in pharmacostatics. We specifically pose two problems about a particular relevant class of networks of reversible binding reactions. The first problem is to exploit a certain fixed-point formulation of the equilibrium equation to devise an algorithmic method that would be compellingly preferable to current practice in the pharmacostatics context. The second problem is to explicitly anticipate the possibility of non-monotone dose-response curves from network topology. Addressing these problems would positively impact biopharmaceutical research, and they have inherent mathematical interest.


Pharmacostatics Receptor pharmacology Non-monotone dose-response curve Equilibrium calculation Polynomial system solving Fixed-point algorithm 

Mathematics Subject Classification

13P15 47H10 47J25 92C42 92C45 



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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.AmgenSouth San FranciscoUSA

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