Controlling Ca2+-Activated K+ Channels with Models of Ca2+ Buffering in Purkinje Cells

Intracellular Ca2+ concentrations play a crucial role in the physiological interaction between Ca2+ channels and Ca2+-activated K+ channels. The commonly used model, a Ca2+ pool with a short relaxation time, fails to simulate interactions occurring at multiple time scales. On the other hand, detailed computational models including various Ca2+ buffers and pumps can result in large computational cost due to radial diffusion in large compartments, which may be undesirable when simulating morphologically detailed Purkinje cell models. We present a method using a compensating mechanism to replace radial diffusion and compared the dynamics of different Ca2+ buffering models during generation of a dendritic Ca2+ spike in a single compartment model of a PC dendritic segment with Ca2+ channels of P- and T-type and Ca2+-activated K+ channels of BK- and SK-type. The Ca2+ dynamics models used are (1) a single Ca2+ pool; (2) two Ca2+ pools, respectively, for the fast and slow transients; (3) detailed Ca2+ dynamics with buffers, pump, and diffusion; and (4) detailed Ca2+ dynamics with buffers, pump, and diffusion compensation. Our results show that detailed Ca2+ dynamics models have significantly better control over Ca2+-activated K+ channels and lead to physiologically more realistic simulations of Ca2+ spikes and bursting. Furthermore, the compensating mechanism largely eliminates the effect of removing diffusion from the model on Ca2+ dynamics over multiple time scales.