Fig 1.
Experimental voltage recordings.
(A1-B1) Spontaneous AP firing in two selected cells. (A2-A3) Close-ups of selected APs from the cell in A1. (B2-B3) Close-ups of selected APs from the cell in A2. (C1) Spontaneous activity before (blue) and after (red) TTX application. (C2-C3) Close-ups of two selected events before (blue) and after (red) TTX application. (D1) Spontaneous activity before (blue) and after (red) paxilline application. (D2-D3) Close-ups of two selected events before (blue) and after (red) paxilline application. The firing rates in the various recordings were 0.64 Hz (A1), 0.57 Hz (B1), 1.22 Hz (C1, before TTX), 0.17 Hz (D1, before paxilline) and about 0.35 Hz (D1, after paxilline). AP width (defined as the time between the upstroke and downstroke crossings of the voltage midways between −50 mV and the peak potential) varied between 3 and 7 ms, with mean width of 3.7 ms (A1), 4.9 ms (B1), 3.7 ms (C1, before TTX). In (D1), average AP widths were 4.2 ms before paxilline. After paxilline, the AP shapes varied, with AP widths ranging from 9 ms to 90 ms, with a mean of 25 ms. AP peak voltages varied between -11.8 mV and +5.5 mV, with mean peak values of −0.4 mV (A1), −3.4 mV (B1), −5.1 mV (C1, before TTX), −3.1 mV (D1, before paxilline), and −6.4 mV (D1, after paxilline). AP width was calculated at half max amplitude between −50 mV and AP peak. The experiments were performed on gonadotroph LH-producing cells in medaka. All depicted traces were corrected with a liquid junction potential of −9 mV. The time indicated below each panel refers to the duration of the entire trace shown.
Fig 2.
(A1) INa in models of a medaka gonadotroph and a generic murine pituitary cell (G). INa had three activation gates (q3) and one inactivation gate (h). (B1) ICa activation in models of medaka gonadotrophs, generic murine pituitary cells (G), rat lactotrophs (RL), and rat somatotrophs (RS). Two activation gates were used in medaka (m2), and one in the other models. (C1) IK had one activation gate (n). (D1) IBK, had one activation gate (f), depending on voltage and domain [Ca2+], the latter assumed to be proportional to ICa. Results shown for ICa = 0, 10, 30 and 100 pA. (E1) ISK was Ca2+ activated with one activation gate s. (A2-B2) Voltage-dependent activation time constants were computed for INa (A2) and ICa (black curves), while all murine model used fixed time constants (red curves). Voltage-independent activation-time constants were used for IK (C2), IBK (D2) and ISK (E2). (A-E).
Fig 3.
The spontaneous activity of the medaka gonadotroph model for different levels of BK-expression. (A1) Spontaneous activity under control conditions, where gBK was maximally expressed (blue curve, gBK = 0.31mS/cm2). AP firing was completely abolished by setting gNa = 0, mimicking the effect of TTX (red curve). (B1-F1) Simulations with gBK reduced to fractions (indicated above panels) of the maximum value. Reductions in gBK consistently lead to broader APs. (A2-F2) Close-ups of the first APs in seen in A1-F1.
Fig 4.
Feature-based sensitivity analysis.
Sensitivity to variations in the maximum ion-channel conductances. The analysis summarizes a large number of simulations where the maximum conductances of all ion channels were varied within intervals ±50% of their original values. An exception was made for gBK, which was varied between 0 and 0.31 mS/cm2. Features were binary (0 or 1), and (A) IsBursting = 1 for simulations that elicited one or more bursts, (B) IsRegular = 1 for simulations that elicited one or more regular APs, and (C) IsNotSpiking = 1 for simulations that did not elicit any AP events. (A-C) Histograms depict the total-order Sobol sensitivity indices which quantify how much of the variability in a response features that is explained by the variation of a given model parameter, including all its co-variances with other parameters. The analysis was performed by aid of the recently developed toolbox Uncertainpy [36] (see Methods for details).
Table 1.
Conductances in the default parameterization of the medaka gonadotroph model.
gBK was varied between simulations, and had values between 0 and the (maximum) value given the table. * gCa had the units of a permeability.
Fig 5.
Effects of IBK on AP shape in different pituitary cell models.
(A) Four versions of the medaka gonadotroph model were studied, differing in terms of the BK activation time constant (τBK). The default parameterization had τBK = 3 ms (orange curve). The inset in A2 shows the same curves as the main panel, but with a wider range on the y-axis. (B) The rat lactotroph model was taken from [9]. (C) The generic murine pituitary cell model was taken from [32]. Two versions were considered, one with (orange curve) and one without (blue curve) sodium conductances added in the model. (D) The rat somatotroph model was taken from [27]. (A1-E1) The AP-peak voltage decayed monotonically with gBK in all models. (A2-D2) An increase in gBK could lead to both a broadening and narrowing of APs, depending on conditions. AP width was defined as the time between the upstroke and downstroke crossings of the voltage midways between −50 mV and the peak potential. (A3-D3) An increase in gBK could cause both stronger or weaker afterhyperpolarization (AHP), depending on conditions. AHP was defined as the minimum voltage reached between two spikes. (A-D) In all panels, the x-axis showed gBK relative to a reference value gBKref, which was taken to be the default BK-conductance in the respective models.
Fig 6.
Action potential upstrokes in different pituitary cell models.
The AP upstroke was steepest in the medaka gonadotroph model (where it was mediated by INa), and slower in the murine pituitary models where they were predominantly mediated by ICa. The models considered were (blue) the default parameterization of the medaka gonadotroph model, (red) the rat lactotroph model, a generic murine pituitary cell model with (purple) and without (orange) sodium conductances, and (green) the rat somatotroph model. In all models, the BK conductance was set to zero.
Fig 7.
Experimentally recorded Na+ currents.
(A) Na+ currents evoked by the activation protocol. (B) Na+ currents evoked by the inactivation protocol. (C) Na+ currents used to determine the time constant for recovery from inactivation. (A-C) Voltage protocols are shown below the recorded currents, and all panels show a series of experiments (traces). In (C), the cell was exposed to a pair of square 10 ms pulses arriving with various inter-pulse intervals (Δt). The first pulse always arrived after 40 ms (and coincided in all experiments), while each secondary spike represents a specific experiment (i.e., a specific Δt). The traces were normalized so that the first spike had a peak value of −1 (corresponding to approximately −0.25 pA).
Fig 8.
Fitted kinetics for the Na+ current.
Voltage dependence of steady-state activation (A), steady-state inactivation (B), activation time constant (C) and inactivation time constant (D). The data points and curves in (A-B) were normalized so that activation/inactivation curves had a maximum value of 1 (assuming fully open channels). Dashed lines represent the same model when corrected for a liquid junction potential of 9 mV.
Table 2.
Parameters for Na+ activation.
The parameters p1-p6 are used together with Eq 22 to yield the time constants for steady state activation and inactivation (in units of ms). The remaining parameters are used together with Eq 20 to obtain the steady-state activation and inactivation functions. The curves obtained in this way describe the voltage dependence under experimental conditions, and was afterwards corrected by subtracting the liquid junction potential of −9 mV (see Fig 2A).
Fig 9.
Fitted kinetics for the Ca2+ current.
(A) ICa evoked by the activation protocol. (B) ICa evoked by the deactivation protocol. (A-B) Voltage protocols are shown below the recorded currents, and all panels show a series of experiments (traces). The current-traces were low-pass filtered with a cutoff-frequency of 300 Hz. (C) Voltage dependence of steady-state activation, normalized so that the activation curve had a maximum value of 1 (assuming fully open channels). (D) Activation time constant. Red data points were estimated from the deactivation protocol (B), while blue data points were estimated using the activation protocol (A). Dashed lines in (C-D) denote the kinetics scheme when corrected for a liquid junction potential of −15 mV for the experimental conditions used for recording Ca2+ currents.
Table 3.
Parameters for Ca2+ activation.
The parameters p1-p6 are used together with Eq 22 to yield the time constants for steady state activation (in units of ms). The remaining parameters are used together with Eq 20 to obtain the steady state activation function. The curves obtained in this way describe the voltage dependence under experimental conditions, and was afterwards corrected with a liquid junction potential of −15 mV (see Fig 2B).