The provided code represents a computational model of neocortical Layer 5b pyramidal neurons, specifically extending the model to incorporate intracellular sodium ion (\([Na^+]\)) dynamics alongside calcium ion dynamics, as inspired by the work of Hay et al. (2011). ### Biological Basis #### Layer 5b Pyramidal Neurons - **Structure and Function**: Layer 5b pyramidal neurons form a critical component of the cortex. They have extensive dendritic trees and long axons that project to various brain regions, playing a crucial role in integrating synaptic inputs and generating action potentials to relay information. #### Ion Dynamics and Active Properties - **Sodium Dynamics ([Na⁺]i)**: - The introduction of intracellular sodium mechanisms suggests a detailed exploration of sodium ion dynamics, particularly their role in action potential generation and propagation. - The code modifies the model to include sodium pumps (`nadp`) and considers various kinetic parameters (`k1_nadp`, `k2_nadp`, `k3_nadp`, etc.), which relate to the activity of sodium ion pumps responsible for maintaining the sodium concentration gradient across the cell membrane. - This inclusion emphasizes the importance of sodium in maintaining resting membrane potential and action potential propagation. - **Calcium Dynamics ([Ca²⁺]i)**: - Calcium ions are pivotal in a range of cellular processes, including synaptic plasticity, neurotransmitter release, and gene expression. - The model incorporates calcium dynamics through `cadp` and `ncx` mechanisms, which simulate calcium ion pumps and exchangers, fundamental to calcium homeostasis. - **Gating Variables**: - The model includes various gating variables (`h`, `m`, `z`, etc.) that describe the state of voltage-gated ion channels, crucial for neuron excitability and the generation of action potentials. #### Temperature and GHK Equation - **Temperature**: - The code sets the simulation temperature to 35°C, approximating mammalian physiological conditions, which significantly impacts ionic conductance and kinetics. - **Goldman-Hodgkin-Katz (GHK) Equation**: - The GHK equation is employed for equilibrium potentials, highlighting the consideration of ionic gradients and their impact on membrane potential. ### Pump and Buffer Systems - **Sodium/Calcium Pumps**: - The code models sodium and calcium pumps to simulate the active transport of these ions across the cellular membrane, emphasizing their role in resetting the ionic concentration after neuronal firing. - **Buffers**: - The model includes buffering systems (`TotalEndBuffer_cadp`) that dynamically regulate intracellular calcium levels, crucial for preventing calcium overload and toxicity. ### Overall Purpose The code aims to simulate the complex electrophysiological behavior of Layer 5b pyramidal neurons by capturing a range of dendritic and perisomatic active properties and the dynamics of key ions, particularly sodium and calcium. Through detailed ion channel and pump modeling, the code seeks to replicate neuronal behavior under different physiological conditions, enhancing the understanding of how these neurons process and relay information in the brain.