# Biological Basis of the Computational Model The code presents a simplified representation of neuronal dynamics based on the Hodgkin-Huxley model, a foundational biophysical model that describes how action potentials in neurons are initiated and propagated through changes in ion conductance. The provided model code specifically configures a planar type-1/type-2 model, which allows researchers to study different neuronal firing patterns and dynamics under controlled conditions. ## Key Elements of the Model ### Ion Channels and Conductances - **Sodium (Na) Channels:** - Described by parameters `gna` (maximum conductance) and `ena` (reversal potential). - Govern action potential initiation and depolarization due to the influx of Na\(^+\) ions. - **Potassium (K) Channels:** - Described by `gk` (maximum conductance) and `ek` (reversal potential). - Responsible for repolarization and maintaining the resting potential, facilitated by efflux of K\(^+\) ions. - **Leak Channels:** - Represented by `gl` and `el`, accounting for non-specific ionic flow that stabilizes the membrane potential at rest. ### Gating Variables - **Activation (`m`):** - Follows a steady-state function `m_\infty(v)`, approximating fast activation of sodium channels as a function of the membrane potential `v`. - Simplified without time dynamics, assuming instantaneous adjustment. - **Inactivation (`n`):** - Governed by `n_\infty(v)` and the time constant `\tau_n(v)`, reflecting the delayed response of potassium channels which stabilize after an action potential peak. - Models are designed to capture the temporal dynamics of channel inactivation and recovery. ### Model Type Dynamics The code can switch between Type-1 and Type-2 excitability patterns: - **Type-1:** Characterized by continuous and gradual response to increasing inputs, allowing the generation of action potentials at low frequencies. - **Type-2:** Exhibits a more abrupt onset of firing at a specific threshold, generating higher frequency responses more readily. These shifts are facilitated by toggling the `type21` parameter, which alters several intrinsic properties such as leak conductance (`gl`, `el`) and other gating-related variables. ### Biological Relevance This model simplification retains biological realism by: - Simulating characteristic action potential features like threshold, spiking rate, and post-spike after-hyperpolarization. - Simulating input resistance dynamics and variations across the two types of neuronal behavior, which affects how neurons respond to incoming synaptic or applied currents. These properties are important for understanding both normal neural processing and the basis for various neural disorders. By providing a straightforward yet robust platform, such models allow for the exploration of fundamental neurodynamic principles, contributing to broader neuroscience applications.