# Biological Basis of the Ball and Stick Model Code The provided computational model is designed to simulate a simplified version of a neuron, often termed a "ball and stick" model. This type of model is used in computational neuroscience to study neuronal behavior and electrophysiological properties. The primary components of this model include a soma (cell body) and a dendritic tree, reflecting the core architecture of neurons. ## Key Biological Features Modeled: ### 1. **Membrane Properties** - **Specific Membrane Capacitance (Cm):** The model uses a value of 1.0 µF/cm², representing the ability of the membrane to store charge. This is critical for simulating the capacitive properties of the lipid bilayer. - **Internal Resistivity (Ri):** Set at 100 ohm-cm, this reflects how easily current flows through the intracellular space. - **Specific Membrane Resistivity (Rm):** Defined as 15000 ohm/cm², it models the resistance of the neuron's membrane to the flow of ionic current through passive (leak) channels. ### 2. **Ionic Channels and Gating** - **Sodium (Na) and Potassium (K) Channels:** These are crucial for action potential generation and propagation. - **Na Channels:** The soma has a channel density of 100 pS/µm², while the initial axonal segments have varied densities, increasing to 8000 pS/µm² in some regions. This simulates the high concentration of sodium channels in the axon initial segment, facilitating action potential initiation. - **K Channels:** Mirror the sodium channels' distribution but with different densities (100 and 2000 pS/µm², respectively). Potassium channels are crucial for repolarization following an action potential. ### 3. **Temperature** - **Celsius:** Set at 37°C, this parameter aligns with typical mammalian body temperatures, ensuring that channel kinetics reflect physiological conditions. ### 4. **Passive Properties** - **Leak Channels (pas):** A passive leak conductance is included, with a conductance (g_pas) set as the inverse of Rm. These channels are crucial for setting the resting membrane potential and allowing for passive current flow. ### 5. **Neuron Architecture** - **Soma:** Represents the neuron’s cell body, housing the nucleus and integrating synaptic inputs. - **Dendrites:** Function to receive synaptic inputs from other neurons, modeled here with adjustable lengths and properties. - **Spines:** Smaller structures protruding from dendrites, they increase the surface area for synaptic inputs and are simulated individually. - **Axon:** Captures the transmission segment of the neuron, essential for carrying action potentials away from the soma to other neurons. The distinct segmentation and channel density changes in the axon initial segment reflect its specialized role in action potential generation. ### 6. **Ionic Concentrations** - **Extracellular Sodium (nao) and Potassium (ek):** Set to 150 mM and -96 mV, respectively, these values are essential for maintaining the ionic gradients necessary for action potential dynamics. ### 7. **Temperature** - All physiological processes are modeled at a temperature of 37°C, reflecting typical mammalian body temperature, to ensure realistic kinetics of the ion channels. This model structure is fundamental in understanding how variations in ionic conductances, compartmental geometry, and passive membrane properties can affect neuronal function, and closely examines the initiation and propagation of action potentials across different parts of the neuron.