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### Equations

The channel conductance was determined by the product of voltage-dependent
activation (m) and inactivation (h) gates, and for the Ca^{2+}-activated channels a
Ca^{2+}-dependent activation gate (z)

| (1) |

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

| (2) |

| (3) |

Activation rates for Ca^{2+}-dependent gates were determined by a dissociation
constant A and a time constant B

| (4) |

| (5) |

For the Ca^{2+} channels the Nernst potential [1] was computed continuously.
Rectification of Ca^{2+} channels was not modeled using the Goldman-Hodgkin-Katz
(GHK) equation [1] because dendritic membrane potentials in this study stayed
within a range where Ca^{2+} 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
( ) to compensate for differences in driving force would cause only small changes
in the amplitude of dendritic Ca^{2+} currents (mean difference 0.7 %, maximum
4.5 %).

### References

[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.