# Biological Basis of the Computational Model The provided code is a computational model designed to simulate the behavior of ion channels in the squid giant axon membrane, building on the foundational Hodgkin-Huxley model. It employs a modified version of the original Hodgkin-Huxley equations to incorporate additional features such as sodium-potassium pumps and variable shifts in channel activation. These modifications are intended to replicate specific neuronal dynamics as referenced in a cited paper by Béla and P.A.B. ## Key Biological Elements ### Ion Channels and Currents - **Sodium Channels (Na⁺):** The model includes standard sodium channels that facilitate the rapid influx of Na⁺ ions, crucial for the depolarization phase of the action potential. There are two sets of gating variables for sodium channels: unshifted (`m`, `h`) and left-shifted (`mLS`, `hLS`), representing different populations of sodium channels with a voltage-dependent shift in activation dynamics. - **Potassium Channels (K⁺):** Potassium channels, responsible for repolarizing the neuron by allowing K⁺ efflux, are also split into normal (`n`) and affected (`nLS`) gating dynamics. This reflects potential populations with altered activation properties. - **Leak Channels:** Account for the passive leak currents due to non-gated channels that maintain resting membrane potential. ### Ion Pumps - **Na-K Pumps:** These are crucial for maintaining the ionic gradients across the membrane by actively transporting Na⁺ out of and K⁺ into the cell, using energy from ATP hydrolysis. This model includes explicit terms for these pumps, calculating the current (`ink`) based on sodium and potassium concentrations. ### Gating Variables The model simulates the time- and voltage-dependent behavior of ion channels through gating variables, following the Hodgkin-Huxley convention: - **Activation (`m`, `mLS` for sodium and `n`, `nLS` for potassium):** Probabilities that the channels are open. These are altered by "left-shift" to explore the effects of varying channel sensitivity and kinetics. - **Inactivation (`h`, `hLS` for sodium):** Probability reflecting the channels closing even if the membrane is depolarized, controlling the duration sodium channels remain open. ### Temperature Adjustment - **Q10 Factor:** Temperature-dependent kinetics are adjusted using a Q10 factor, emphasizing that biological rates may vary with temperature, replicating conditions (e.g., squid axon physiology) typically at lower temperatures around 6.3°C. ## Summary This modified Hodgkin-Huxley model extends the classical framework by adding left-shift functionalities for a subset of sodium and potassium channels to explore their effects on neuronal excitability and dynamics. The introduction of Na-K pumps aims to provide a more physiologically realistic representation of ionic homeostasis in neurons, complementing the set of traditional ion channels. This combination seeks to improve the model’s alignment with empirical observations as cited in the reference paper.