The provided code models the dynamics of a neuronal network using the Hodgkin-Huxley formulation, which is a well-established framework for describing how action potentials in neurons are initiated and propagated. Here's a breakdown of the biological basis of key components observed in the code: ### Ion Channels and Ions 1. **Sodium (Na\(^+\)) Channels:** - **Reversal Potential (`ena`)**: The value `55.0` mV represents the reversal potential for sodium ions, which is crucial for action potential generation as the influx of Na\(^+\) depolarizes the neuron. - **Conductance (`gna`)**: `35.0` represents the maximal conductance of sodium channels. - **Gating Variables (`h`) and Activation/Deactivation (`am`, `bm`, `ah`, `bh`)**: These functions define the voltage-dependent opening (activation) and closing (inactivation) dynamics of Na\(^+\) channels. The inactivation variable `h` affects how many sodium channels are available to open. 2. **Potassium (K\(^+\)) Channels:** - **Reversal Potential (`ek`)**: Set at `-90.0` mV, this is the equilibrium potential for K\(^+\), and it's critical for repolarizing the neuron following an action potential. - **Conductance (`gk`)**: The value `9.0` denotes the maximal conductance of potassium channels. - **Gating Variables (`n`) and Activation/Deactivation (`an`, `bn`)**: These functions regulate the opening and closing of K\(^+\) channels, allowing for the outflux of K\(^+\) that repolarizes the neuron. 3. **Leak Channels:** - **Reversal Potential (`el`)**: `-65.0` mV is used for leak channels, allowing small, constant flows of ions to maintain the resting membrane potential. - **Conductance (`gl`)**: Represents small, non-voltage dependent leak conductance (`0.1`). ### Synaptic Transmission - **Synaptic Gating Variable (`s`)**: Represents the synaptic state, which is affected by an excitatory conductance (`ae`) and a decay term over tau (`taus`), simulating synaptic dynamics. - **Synaptic Reversal Potential (`esyn`)**: `-75.0` mV, often associated with inhibitory post-synaptic potentials in biological neurons. - **Synaptic Conductance (`gsyn`)**: Refers to the strength of synaptic connections. - **Weight Matrices (`W`, `W1`)**: Used to represent synaptic connectivity and strength between neurons before and after a midpoint time (`T_mid`). ### External Inputs - **Applied Current (`Iapp`)**: Simulates external stimuli or inputs to the neuron. - **Perturbation (`Ip`, `Tp`)**: Introduces temporally controlled paddle applications to simulate additional current inputs during specified intervals (`Tp`). ### Temperature Coefficient (`phi`) - **Phi Factor**: Indicates the temperature sensitivity or adjustment for the rate of gating variable dynamics. A value of `1.0` suggests standard conditions. ### Biological Context Overall, this code models the electrical activity of a network of biological neurons, capturing the dynamics of action potentials through the interplay of ionic channels and synaptic inputs as modeled by differential equations. Each neuron's state is described by its membrane potential (`v`) and the gating variables associated with ion channels, reflecting complex physiological interactions at synaptic and intrinsic levels.