Estradiol elicits distinct firing patterns in arcuate nucleus kisspeptin neurons of females through altering ion channel conductances

Hypothalamic kisspeptin (Kiss1) neurons are vital for pubertal development and reproduction. Arcuate nucleus Kiss1 (Kiss1ARH) neurons are responsible for the pulsatile release of Gonadotropin-releasing Hormone (GnRH). In females, the behavior of Kiss1ARH neurons, expressing Kiss1, Neurokinin B (NKB), and Dynorphin (Dyn), varies throughout the ovarian cycle. Studies indicate that 17β-estradiol (E2) reduces peptide expression but increases Vglut2 mRNA and glutamate neurotransmission in these neurons, suggesting a shift from peptidergic to glutamatergic signaling. To investigate this shift, we combined transcriptomics, electrophysiology, and mathematical modeling. Our results demonstrate that E2 treatment upregulates the mRNA expression of voltage-activated calcium channels, elevating the whole-cell calcium current and that contribute to high-frequency burst firing. Additionally, E2 treatment decreased the mRNA levels of Canonical Transient Receptor Potential (TPRC) 5 and G protein-coupled K+ (GIRK) channels. When TRPC5 channels in Kiss1ARH neurons were deleted using CRISPR, the slow excitatory postsynaptic potential (sEPSP) was eliminated. Our data enabled us to formulate a biophysically realistic mathematical model of the Kiss1ARH neuron, suggesting that E2 modifies ionic conductances in Kiss1ARH neurons, enabling the transition from high frequency synchronous firing through NKB-driven activation of TRPC5 channels to a short bursting mode facilitating glutamate release. In a low E2 milieu, synchronous firing of Kiss1ARH neurons drives pulsatile release of GnRH, while the transition to burst firing with high, preovulatory levels of E2 would facilitate the GnRH surge through its glutamatergic synaptic connection to preoptic Kiss1 neurons.


Persistent sodium current:
݃ ே is the maximum conductance; ݄ ே is the corresponding inactivation gating variable that obeys the following equation: and the steady-state activation and inactivation functions are given by: The above description of the persistent sodium current was taken from a model of the GnRH neuron [3].

A current:
‫ܫ‬ ൌ ݃ • ݉ • ݄ • ሺܸ െ ‫ܧ‬ ሻ ݃ ே denotes the maximum conductance; ‫ܧ‬ is the potassium reversal potential; and ݉ and ݄ are the corresponding activation and inactivation gating variables, which are described by the following equations: .
The steady-state activation and inactivation functions are given by: The model of the A-current was based on Mendonca's model of Kv4 channels [4], as these channels are also found in Kiss1 ARH neurons [5].

BK current
Here, ݃ is the maximum conductance; and ܾ ,ஶ ሺܸ , ܿሻ is the steady-state activation function that depends on the membrane potential, ܸ , as well as on the cytosolic calcium concertation, ܿ: The model of the BK-current was based on the model presented in [6], with the conductance parameter fitted to the current-voltage relationships recorded from Kiss1 ARH neurons in the absence and presence of the specific BK blocker, iberiotoxin.

SK current
݃ ௌ denotes the maximum conductance; and ܾ ௌ,ஶ ሺܿሻ is the steady-state activation function, which depends on the cytosolic calcium concertation, ܿ: The model of the BK-current was based on the model presented in [7], with the conductance fitted to the currentvoltage relationships recorded from Kiss1 ARH neurons in the absence and presence of the specific SK blocker, apamin.

M current
݃ ெ denotes the maximum conductance, and ݉ ெ is the corresponding activation gating variable: with the steady-state activation function, ݉ ெ,ஶ ሺܸ ሻ, taking the form: The model of the M-current was parameterised using the steady-state voltage-clamp measurements from actuate Kiss1 neurons [8], while for the activation timescale we used the timescale used in a model of the CA1/3 pyramidal cells [9].
݃ denotes the maximum conductance; and ݉ ,ଵ and ݉ ,ଶ are separate activation gating variables operating on different timescales (߬ ,,ଵ and ߬ ,,ଶ respectively): The corresponding steady-state activation functions are: Finally, parameter ‫‬ dictates the relative contribution of and ݉ ,ଵ and ݉ ,ଶ to the total current.This model of the h-current is based on the hippocampal CA1 pyramidal neuron [7].
To model of the T-current was based on AVPV kisspeptin neurons data presented in [2,10].

L-, N-, P/Q-, R-type calcium currents
݃ denotes the maximum conductance; and ݉ and ݄ are the corresponding activation and inactivation gating variables, which are described by the following equations: The steady-state activation and inactivation functions are given by: Parameters of the model for the high voltage activated calcium channels were calibrated from the current-voltage relationships obtained from Kiss1 ARH neurons (see Figure 2 and 6 of the main text).

TRPC5 current
݃ ்ோହ denotes the maximum conductance; and ܾ ்ோହ ሺܿ, ܴ ்ோହ,௧ ሻ the activating gating variable that depends both on cytosolic calcium concertation (ܿሻ and on NKB-mediated activation of an intermediary effector, ܴ ்ோହ,௧ [11]: The dynamics of ܴ ்ோହ,௧ (activated form of ܴ ்ோହ ) are described by: ܴ݀ where NKB is the extracellular NKB concertation; ݇ ோ, is the basal rate of ܴ ்ோହ activation; ݇ ோ is the maximal rate of ܴ ்ோହ activation in the presence of NKB; ݇ ିோ is the rate of ܴ ்ோହ inactivation; and ܴ ்ோହ,் is the total concentration of the effector.

GIRK current
݃ ீூோ denotes the maximum conductance; and ܾ ீூோ ሺܸ , ܴ ீூோ,௧ ‫ܤ‬ሻ the activating gating variable that depends on membrane potential, ܸ , and on external activation of an intermediary effector, ܴ ீூோ,௧ : The dynamics of ݉ ீூோ are described by: ݀݉ ீூோ ‫ݐ݀‬ ൌ ݉ ீூோ,ஶ ሺܸ ሻ െ ݉ ீூோ ߬ ீூோ ሺܸ ሻ where the steady state activation function and timescale function are given by: The dynamics of ܴ ீூோ,௧ are described by: ܴ݀ where s is the extracellular concertation of the activation signal.
The model and parameters of the GIRK current is taken from [12].

Leak currents
The leak current parameters were calibrated to current-voltage relationships recorded from Kiss1 ARH neurons in the absence/presence of iberiotoxin (BK blocker) and apamin (SK blocker).

Intracellular calcium dynamics
Finally, the intracellular calcium dynamics are described via the following equation: where parameter ߛ converts the currents to molecule fluxes and parameter ݀ dictates the linear rate at which calcium is depleted or pumped out of the cell.

Modelling the effect of E2
The effect of E2 on ionic currents is modelled as a change in the maximum conductance parameter.For currents ‫ܫ‬ ெ , ‫ܫ‬ ் , ‫ܫ‬ and ‫ܫ‬ ்ோହ this change is inferred from the qPCR data assuming that the conductance is directly proportional to the mRNA expression.For ‫ܫ‬ ௌ , ‫ܫ‬ , ‫ܫ‬ , the OVX and OVX+E2 conductances are obtained from current-voltage relationships recorded from Kiss1 ARH neurons in the absence/presence of iberiotoxin (BK blocker) and apamin (SK blocker).All other currents were assumed to be unaffected by E2.Parameter ‫ܥ‬ in calibrated using direct measurements of the membrane conductance in the OVX and OVX+E2 state.For the simulation presented in the Figure 13 of the main text, conductances were varied within ranges that captures the physiological effect of E2.

Computer simulations
Integration of the differential equations describing the model was carried out in MATLAB R2023b using a standard 4th order Runge-Kutta method.Parameter fitting was also conducted in MATLAB R2023b using the least squares curve fitting method.

Figure S1 .1
Figure S1.Schematic diagram of the conductance based mathematical model of Arcuate nucleus Kiss1 neurons.

Table S1 Table
of model parameters.