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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)

        2+               p     2+    r
G(V, [Ca    ],t) = ˉgm(V, t) z([Ca   ],t) , (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) = ---------------, βm(V, t) = ---------------, idem  for αh and  βh
           B +  expV+C)∕D              F + exp(V +G)∕H

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

∂z-=  z∞---z-
∂t      τz

z∞ =  1 + ---A---τz = B

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