GENESIS: Documentation

Related Documentation:

De Schutter: Purkinje Cell Model


The channel conductance was determined by the product of voltage-dependent activation (m) and inactivation (h) gates, and for the Ca2+-activated channels a Ca2+-dependent activation gate (z)

G(V, [Ca2+], t) = ˉgm(V, t)pz([Ca2+],t)r, (units: mV,  μM,  ms)

Equations describing the voltage-dependent gates were described from the classic Hodgkin-Huxley [2] scheme

----= αm(1  - m) -  βmm,  idem  for h

                  A                           E
αm(V, t) = --------V+C)∕D-, βm(V, t) = --------(V-+G)∕H, idem  for αh and  βh
           B +  exp                    F + exp

Activation rates for Ca2+-dependent gates were determined by a dissociation constant A and a time constant B

∂z    z∞ - z
---=  -------
∂t      τz

z∞ =  -------A---τz = B
      1 + [Ca2+]

For the Ca2+ channels the Nernst potential [1] was computed continuously. Rectification of Ca2+ channels was not modeled using the Goldman-Hodgkin-Katz (GHK) equation [1] because dendritic membrane potentials in this study stayed within a range where Ca2+ channels can be considered ohmic (i.e., below -20 mV; Fig. 4.15 in [1] ). Using the simulation results from the final model, we estimate that using the GHK equation with an appropriately scaled maximum conductance (ˉg ) to compensate for differences in driving force would cause only small changes in the amplitude of dendritic Ca2+ currents (mean difference 0.7 %, maximum 4.5 %).


[1]   B Hille. Ionic Channels of Excitable Membranes. Sunderland MA: Sinauer, 1991.

[2]   Hodgkin A L and Huxley A F. A quantative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology (Lond.), 117:500–544, 1952.