Biological Basis of the Model

The provided code represents a model of neuronal ion channel dynamics, specifically focusing on the delayed rectifier potassium (K(^+)) channels. These channels play a crucial role in the action potential repolarization phase in neurons.

Key Biological Components

Delayed Rectifier Potassium Channels (K(^+) Channels)

• Function: These channels are responsible for returning the membrane potential back to its resting state following an action potential. They help facilitate the repolarization phase by allowing the efflux of K(^+) ions.
• Properties: The kinetics of these channels are often slower compared to other types, such as transient potassium channels. The "delayed" aspect indicates their slower activation in response to membrane depolarization.

Ionic Currents and Conductance

• Potassium Ion (K(^+)) Current ((i_k)): This is the current through the potassium channels, essential for repolarizing the membrane potential.
• Conductance ((g_{kdr})): This parameter determines how many ions can pass through the channels at any given time, directly influencing the current. It is typically expressed in millisiemens per square centimeter (mS/cm(^2)).

Gating Variables

• Activation Variable (n): Represents the probability of the K(^+) channels being open. This variable transitions based on the membrane potential ((v)), and is governed by the functions defined within the rates procedure.
• Steady-state Activation ((n_{inf})): Defines the fraction of channels that would be open at a particular membrane potential if it were held constant indefinitely.
• Time Constant ((\tau_n)): Represents how quickly the activation variable ((n)) approaches its steady state value. The inverse relationship to channel gating rates in the model reflects the channel's opening and closing speed.

Membrane Potential and Reversal Potential

• Membrane Potential ((v)): The electrical potential difference across the neuron's membrane, influencing the opening and closing of ion channels.
• Potassium Reversal Potential ((e_k)): The equilibrium potential for potassium ions, set at -75 mV in the model, indicates the potential at which there is no net flow of K(^+) ions across the membrane.

Biological Computation

The model incorporates a computational implementation of the gating kinetics using procedures like rates and states. These govern how the activation variable (n) evolves over time based on current membrane potentials.

• Rate Functions (a, b): This model uses auxiliary functions (fun1, fun3 defined in "aux_fun.inc") to simulate the voltage-dependent opening and closing of channels.
• Differential Equations: Govern the time evolution of the gating variable based on its current value and steady-state behavior.

This model is significant for understanding the behavior of neurons during electrical signaling, specifically how neurons reset their membrane potential after an action potential to prepare for subsequent signaling events.