Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells

Calcium (Ca(2+)) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP(3))-induced Ca(2+) release. These Ca(2+) transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca(2+), requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca(2+) transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca(2+) transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca(2+) transients in different dynamical situations. We test two different models of the IP(3) receptor (IP(3)R). The model with nonlinear concentration response of binding of activating Ca(2+) reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca(2+)-dependent inhibition of the IP(3)R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca(2+) and IP(3) production sensitizing IP(3)R for Ca(2+)-induced Ca(2+) release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca(2+) transients. Finally, we propose possible ways of recovering Ca(2+) transients under ataxia.