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

Abstract

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.Electronic supplementary materialThe online version of this article (doi:10.1007/s12311-010-0224-3) contains supplementary material, which is available to authorized users.

After-hyperpolarization currents and acetylcholine control sigmoid transfer functions in a spiking cortical model

“…The L-type, N-type and P-type currents differ in the voltage threshold of activation and in their inactivating properties. Activation and inactivation equations, shown in Table 2, are derived from measurements of pyramidal cells in sensorimotor neocortex (Brown et al 1993), and correspond to other studies on calcium currents (Anwar et al 2010;Delcour et al 1993;King and Meriney 2005;Lorenzon and Foehring 1995;Luvisetto et al 2004;Wilson et al 2004). …”

“…To capture this specificity, the model includes local somatic calcium concentrations near sources and a cytosolic calcium concentration. The model of calcium dynamics is based on previous models (Anwar et al 2010; Barkai and Hasselmo 1994;Canavier et al 2007;Wang et al 2003;Wilson et al 2004). The cytosolic calcium, [Ca C ] in mM, follows the equation:…”

“…which tends toward a resting calcium concentration, [Ca R ]= 10 −6 mM=1 nM (Abel et al 2004;Anwar et al 2010;Lorenzon and Foehring 1995), at a rate, b c =1/(80 ms). The diffusion rate, δ C =1/(800 ms), defines the exchange rate between the other calcium concentration pools.…”

“…Equations for its calcium-dependence are detailed by Cox et al (1997) based on analysis of physiological recordings and used by Anwar et al (2010). We also employ their equations (see Table 2).…”

“…The channel population is originally set to the lowest closed state (C 1 =1, other states=0). This channel scheme has also been used in other models (Anwar et al 2010;Traub et al 2005;2003).…”