# Biological Basis of the Code The provided code models the relationship between magnesium (Mg²⁺) concentration and voltage-dependent channel conductance, relevant to synaptic transmission in neurons, specifically in NMDA (N-methyl-D-aspartate) receptors. Here, I will outline the biological basis and relevance to neuroscience. ## NMDA Receptors and Magnesium Block ### NMDA Receptors: NMDA receptors are a type of ionotropic glutamate receptor found in neurons' synapses. They are critical for synaptic plasticity, which is fundamental for learning and memory. These receptors are unique due to their voltage-dependent block by extracellular Mg²⁺ ions and their requirement for both ligand binding (glutamate and glycine) and membrane depolarization to conduct ions. ### Magnesium Block: 1. **Voltage Dependence**: At resting membrane potentials, NMDA receptors are blocked by Mg²⁺. When the neuron depolarizes (becomes less negative inside), Mg²⁺ is expelled from the channel, allowing Na⁺ and Ca²⁺ to enter the neuron. This voltage-dependent block is reversible and dynamic. 2. **Biophysical Modeling**: The block of NMDA receptor channels by extracellular Mg²⁺ can be described using equations that consider the voltage across the membrane and the concentration of Mg²⁺. In the provided code, the function `eq_5_fitting_mM` models the probability of the channel being unblocked, which depends on voltage (V) and Mg²⁺ concentration (conc). 3. **Critical Parameters**: The code utilizes specific parameters (e.g., alpha and eta) which relate to how the channel blocking/unblocking process depends on voltage and Mg²⁺ concentration. These parameters are derived from experimental data. ## Experimental Data: The code uses data from experimentally measured voltage-concentration relationships in several studies (e.g., Nowak et al., 1984; Jahr and Stevens, 1990; Chen et al., 1992; McMenimen et al., 2006). The experimental data help to validate the modeled relationship between voltage and Mg²⁺ concentration. ### Key Visualizations: - **Voltage-Concentration Plots**: These demonstrate how varying extracellular Mg²⁺ concentrations influence the voltage necessary to achieve half-maximal conductance through the NMDA receptor. - **Conductance-Voltage Relationship**: Displays how channel conductance varies as a function of membrane voltage at different magnesium concentrations, highlighting the characteristic Mg²⁺ block. ## Summary The code simulates how different concentrations of Mg²⁺ affect the membrane voltage required for NMDA receptor activation, by depicting both the biological and biophysical properties of this critical voltage-dependent ion channel. This simulation aids in understanding how synaptic strength and plasticity are modulated in the brain, foundational for processes such as learning and memory. The use of historic experimental data enhances the fidelity of the model, making it a valuable tool for exploring NMDA receptor behavior under various physiological and experimental conditions.