Simulation of generation–collection experiments with homogeneous kinetics: application to electrochemical investigation of superoxide radical anion generation by osteoclasts on bone

Abstract

We report simulations of electrochemical generation–collection experiments in which the generator is a small disc producing a specified time-dependent flux of the analyte and the collector is a large planar electrode which collects the analyte at the mass transport-controlled rate. This geometry corresponds to many experiments in bioelectrochemistry where a relatively large sensor is used to detect the products of a cell's metabolism at low concentration. In particular, our simulations are motivated by attempts to understand our results on the detection of the superoxide radical anion burst generated by osteoclasts (bone-resorbing cells) in response to various stimuli. Superoxide is present at low levels and disproportionates in aqueous media; however, the homogeneous kinetics are included in our simulations and the results show that it is possible to estimate the magnitude of the flux of superoxide produced by the cells and to accurately determine the time-dependence of the flux in response to stimuli such as injection of parathyroid hormone, vitamin D₃ and pertussis toxin. In all these cases, the superoxide anion flux was successfully modeled as uniform across the cell surface with time-dependence of the form j₀e^−k_dt + j_∞. j_∞ is the sustained flux of superoxide and the first-order rate constant k_d and the magnitude j₀ describe the transient component of the flux. The simulations indicate that for cell–electrode gaps , where D is the diffusion coefficient, the value of k_d can be accurately extracted from the time-dependence of the collector current without detailed knowledge of parameters which are hard to measure during the experiment, e.g., the cell radius a and cell–electrode separation d. In the case of parathyroid hormone, the first-order rate constant describing the decay of the transient component was k_d = 1.8 ± 0.8 × 10⁻¹ s⁻¹, but much slower decays were observed in response to pertussis toxin (k_d = 1.5 ± 0.5 × 10⁻² s⁻¹) and vitamin D₃ (k_d = 1.1 ± 0.5 × 10⁻³ s⁻¹).