Ca²⁺ mechanisms, present mainly on the dendritic tree of cerebellar Purkinje cells (PC) [1], significantly influence its activity pattern [2, 3], synaptic integration [4], etc. Particularly, the intracellular dynamics controlling Ca²⁺concentrations can play a crucial role in the physiological interaction between the Ca²⁺ channels and Ca²⁺-activated K⁺ (KCa) channels [5]. The simplest, but commonly used model, the Ca²⁺ pool with a short relaxation time, will fail to simulate interactions occurring at multiple time scales. On the other hand, detailed computational models including various Ca²⁺ buffers and pumps [6] can result in large computational cost due to radial diffusion in large compartments, which may need to be avoided when simulating morphologically detailed PC models.

We present a method using compensating mechanisms to replace radial diffusion and compared the dynamics of different Ca²⁺ buffering models during generation of dendritic Ca²⁺ spikes during somatic bursting or depolarization [1]. As for the membrane mechanisms, we used a recently constructed single compartment model of a PC dendritic segment with the Ca²⁺ channels of P- and T-type and KCa channels of BK- and SK-type, which can generate the Ca²⁺ spikes comparable to the experimental recordings [7]. The Ca²⁺ dynamics models are (i) a single Ca²⁺ pool, (ii) two Ca²⁺ pools respectively for the fast and slow transients, (iii) detailed Ca²⁺ dynamics with calbindin, parvalbumin, pump and diffusion, and (iv) detailed Ca²⁺ dynamics with calbindin, parvalbumin, pump and diffusion compensation [6]. The simulated membrane voltage was compared with electrophysiological data.

Our results show that detailed Ca²⁺ dynamics models with buffers, pumps, and diffusion have significantly better control over Ca²⁺ activated K⁺ channels and lead to physiologically more realistic simulations of Ca²⁺ spikes. Furthermore, the effect on Ca²⁺ dynamics of removing diffusion from the model can largely be eliminated by the compensating mechanisms. Therefore, physiologically realistic Ca²⁺ concentration dynamics can be simulated at reasonable computational cost.