# Biological Basis of the Computational Model This code is modeling the electrophysiological behavior of neuronal cells, particularly focusing on the dynamics of ion concentrations and membrane potentials under physiological and pathological conditions. ## Key Biological Components ### Membrane Potential and Gating Variables - **Membrane Potential (`V`)**: The potential difference across the neuron's membrane, crucial for action potential propagation. It's affected by the flow of ions through channels. - **Gating Variables (`n`, `h`)**: These represent the probabilistic states of ion channels (potassium and sodium channels, respectively) opening and closing. They are essential for defining how the membrane potential responds to stimuli. ### Ion Concentrations - **Intracellular Ion Concentrations (`ki`, `cli`)**: The concentrations of potassium and chloride inside the cell, which influence the membrane potential and are fundamental to maintaining cellular homeostasis. - **Extracellular and Intracellular Sodium (`NAI`, `NAE`) and Potassium (`KE`)**: These reflect the currents that drive electrical activity in neurons, specifically through the Nernst potentials which dictate the equilibrium potential for each ion. ### Ionic Currents - **Leak and Gated Currents (`INA_l`, `INA_g`, `IK_l`, `IK_g`, `ICL_l`)**: Reflect different types of ionic flows through the membrane. Sodium and potassium channels have both leak (constant) and gated (voltage-dependent) currents, while chloride has only a leak current. - **Na/K-Exchange Pump (`IP`)**: Represents the energy-dependent pump maintaining the sodium and potassium gradients across the membrane, crucial for neuron function under normal and stress conditions. ### Nernst Potentials - Calculated for each ion (`EK`, `ENA`, `ECL`) to determine the driving force for ion movement across the membrane based on their concentration gradients. ## Biological Processes 1. **Hodgkin-Huxley Model Adaptation**: This model is grounded in classic Hodgkin-Huxley dynamics describing how action potentials in neurons are initiated and propagated. Variables like `AN`, `BN`, `AM`, `BM`, `AH`, and `BH` are parameters in the gating equations derived from this model, dictating how channels open and close in response to voltage changes. 2. **Mass Conservation**: It models the extracellular space dynamics by mass conservation laws, showing how ions are exchanged between intra- and extracellular spaces while maintaining electroneutrality. 3. **Fixed Point Continuation**: Investigates the system's behavior under varying conditions, identifying stable states (fixed points) and transitions, such as bifurcations that could represent shifts from normal to pathological activity states. 4. **Ischemic Condition Simulation**: The use of parameters like extracellular volume (`vle`) and `par vle` adjustments, highlight how changes in extracellular environment (e.g., during ischemia) influence ion dynamics and neuronal excitability. Overall, the model captures the fundamental biophysical processes involved in neuronal excitability and how these can be perturbed under pathological conditions such as ischemic injury.