Design of optimally sparse dosing strategies for neural pharmacology

Modeling the actions of neuroactive drugs has typically been limited to two classes of mathematical descriptions: the so-called pharmacokinetics model, which describes the diffusion of the drug from the administration site to the effect site, i.e., the brain; and the pharmacodynamics model, which describes the mapping between effect site concentration and behavioral phenotype. Often, a desired behavioral outcome occurs at the end of the admissible concentration range such as unconsciousness induced via a general anesthetic. Here, we develop a dynamical systems-based modeling and design paradigm to optimally construct pharmacologic regimes, i.e., drug selection and dose schedules, to meet phenotypic objectives while minimizing costs and adverse effects. Our framework focuses less on the kinetics of the drug from infusion to effect site, and more on the explicit descriptions of the affinity of the drugs to their respective molecular targets. Through this paradigm, we use methodologies embedded in formal optimal control theory to show how one can, in a principled manner, optimize selection and dosing of synergistic drugs to efficiently achieve a particular phenotype while mitigating paradoxical or undesired states that might otherwise be encountered.