Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca
2+
concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na
+
currents (
I
Na
), high-voltage activated Ca
2+
currents (
I
Ca
), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where
I
Na
is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by
I
Ca
. Unlike in rats, spontaneous
I
Na
-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (
Oryzias latipes
). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by
I
Na
, and (3) the first pituitary cell model where the kinetics of the depolarizing currents,
I
Na
and
I
Ca
, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire
I
Ca
-based APs. We put a particular focus on how the big conductance K
+
current (
I
BK
) modulates the AP shape. Interestingly, we find that
I
BK
can prolong AP duration in models that fire
I
Ca
-based APs, while it consistently shortens the duration of the predominantly
I
Na
-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire
I
Na
-mediated APs.