Predicting Cocaine Self‐Administration Behavior with Simple Receptor‐Based Pharmacokinetic/Pharmacodynamic Mathematical Models

Cocaine self‐administration behavior is marked by regular inter‐injection intervals that increase nonlinearly in a dose‐dependent manner [1] and can be predicted mathematically by the equation: T = ln(1+Du/Dst)/k, where T is the time between successive self‐administrations, Du is the cocaine unit dose administered at each lever press, Dst is the maximum agonist concentration that induces a lever press (satiety threshold), and k is the first‐order elimination rate constant for the agonist [2]. While useful, the pharmacokinetic parameter (k) and the pharmacodynamic parameter (Dst) should be expanded to include their underlying mechanisms. Cocaine Dst is hypothesized to correspond to a minimum number of dopamine‐receptor complexes and k results from multi‐compartment pharmacokinetics. These parameters are difficult to measure directly in vivo but can be elucidated by mathematical modeling. One‐ and two‐compartment models that express Dst in terms of dopamine receptor occupancy were created using SimBiology in MATLAB. Cocaine's half‐life (t 1/2 ) and affinity for the dopamine transporter (K D ) were varied based on maximum and minimum values from literature. SimBiology scans allow parameter value ranges to be entered and produced simulations corresponding to permutations of the values within those ranges. One scan was run for each cocaine unit dose studied experimentally (300 – 12,000 nmol/kg). Simulations producing values for T accurate to within three standard deviations of experimental data were identified. All simulations qualitatively mirrored the inter‐injection intervals' regularity and nonlinear dose dependency, but only one of the 250 one‐compartment simulations was accurate to within three standard deviations for all five unit doses. Preliminary simulations produced by the two‐compartment model replicate experimental data better than the one‐compartment model at low doses (300 – 3000 nmol/kg) but underestimate experimental data at higher doses (12,000 nmol/kg) ( Figure 1). These simulations were produced using parameter values in pharmacologically relevant ranges ( Table 1). The receptor‐based pharmacokinetic/pharmacodynamic models simulating cocaine self‐administration behavior qualitatively described experimental data, including the inter‐injection intervals' regularity and nonlinear unit dose‐dependency, demonstrating this approach's feasibility. The low number of accurate simulations implies there are strict limitations on the values for parameters underlying cocaine self‐administration, indicating the values used by the models may be predictive of the values for t 1/2 and K D in vivo. Hence, an apparently complex behavior can be accurately described by relatively simple mathematical models incorporating only pharmacological parameters. Support or Funding Information This research was supported by NIDA grant 1U01DA039550‐01 and ASPET. 1 The parameter values used to create accurate one‐ and two‐compartment model simulations.t 1/2 (s) K D (nM) D st (nM)One‐Compartment Simulation 133.33 1829.25 23.97Two‐Compartment Simulation A 300 57 0.004Two‐Compartment Simulation B 300 5352 0.0001