The provided code models the dynamics of a Hodgkin-Huxley based model neuron with certain specific adaptations for examining the effects of sodium and potassium ion availability on neuronal firing. Here is a biological interpretation of the key elements in the code: ### Hodgkin-Huxley Model - **Neuronal Model**: The code implements a modified Hodgkin-Huxley (HH) model. The HH model is a classical representation of the electrical characteristics of excitable cells, like neurons. It describes how action potentials (APs) in neurons are initiated and propagated through the regulation of ion channels. - **Ion Channels & Gating Variables**: The model incorporates sodium (Na+) and potassium (K+) channels, which are essential for action potential generation. The variables `m`, `h`, and `n` are gating variables derived from the biophysical model developed by Hodgkin and Huxley that describes the probability of channel opening: - `m` (activation parameter for sodium channels) - `h` (inactivation parameter for sodium channels) - `n` (activation parameter for potassium channels) ### Adaptations in the Model - **Slow Inactivation of Sodium Channels**: The model includes slow inactivation of sodium channels (`s1`) and is influenced by certain kinetic parameters (`phi_s1`, `amp`, etc.). Slow inactivation is a process that impacts neurons' ability to maintain excitability over time and is a crucial component in explaining repetitive firing and adaptation in neural computations. - **Neurotransmitter Release Dynamics**: The code also introduces a synapse model controlled by neurotransmitter release dynamics, which are modeled by parameters `tau_inact`, `tau_rec`, and `U_se`. These represent synaptic facilitation and depletion dynamics observed in actual synaptic transmission. ### Biophysical Context - **Ion Currents**: The core of the model revolves around simulating ion currents through the neuron membrane: - `gNa`, `gK`, and `gL` are the conductance values for sodium, potassium, and leak channels, respectively. These represent the maximum possible conductances if all gates are open. - `VNa`, `VK`, and `VL` represent the reversal potentials for sodium, potassium, and leak currents, respectively. - **Capacitance and Temperature Factor**: `Cm` is the membrane capacitance per unit area, adjusted for temperature (`phi_HH`). This reflects the neuron's ability to store charge and represents the passive electrical properties of the neuronal membrane. - **Noise and Variability**: The model includes stochastic terms (`noise`, `noise_s`, `N`, `N_s`) applying to gating dynamics and synaptic release processes, introducing variability similar to natural neuronal firing patterns affected by random synaptic input or intrinsic channel noise. ### Simulation Goals - **Exploration in Response to Current Pulses**: The code simulates the response of neurons to a fixed-length current pulse by varying the amplitude of stimulation current (`I0`) and sodium and potassium availability (`s1`, `R`). - **Metrics of Interest**: - **Action Potential (AP) Initiation**: The model examines the conditions under which an action potential is triggered, based on crossing a voltage threshold (`v_threshold`). - **Latency and Spiking Probability**: It measures the latency from stimulus onset to peak voltage (spike timing) and calculates the probability (`p(s)`) that stimulation results in firing, thus helping to understand how these parameters affect neuronal excitability and spiking behavior. This biological model provides a framework to study the dynamic behaviors of neurons under various physiological conditions, offering insights into factors that regulate neuronal firing and synaptic integration.