The provided code models synaptic transmission at an NMDA receptor, a specific type of ionotropic glutamate receptor that plays a critical role in synaptic plasticity, memory formation, and other neural computations in the brain. The NMDA receptor is famously characterized by its voltage-dependent blockade by magnesium (Mg²⁺) ions and its permeability to calcium (Ca²⁺) ions, in addition to sodium (Na⁺) and potassium (K⁺) ions. ### Biological Basis 1. **NMDA Receptors:** - **Glutamate Binding and Ion Flow:** NMDA receptors are activated by the binding of the neurotransmitter glutamate. This binding facilitates ion flow through the receptor's associated channel. - **Mg²⁺ Block:** NMDA receptors have a unique voltage-dependent block by Mg²⁺ ions. At resting membrane potentials, Mg²⁺ ions block the channel. Upon depolarization, this block is relieved, allowing ions to flow through. 2. **Synaptic Conductance Dynamics:** - **Dual-Exponential Kinetics:** The receptor's response is modeled using two exponential states (rise and decay). The `tau1` and `tau2` parameters represent the rise and decay time constants of the synaptic conductance, respectively. This captures the characteristic rise and fall of postsynaptic potentials due to transient receptor activation. - **Conductance Calculation:** The model employs state variables to simulate the binding dynamics of the receptor and the transition to open states through rate equations, which reflect the biological processes of synaptic conductance changes. 3. **Magnesium Block Model:** - The code incorporates the Mg²⁺ block using a mathematical formulation that accounts for voltage-dependent changes (`gamma`) in Mg²⁺ affinity (`mag`) relative to a constant (`eta`). This part reflects the well-known blocking effect of extracellular magnesium on NMDA channels, which only lifts when the neuron is depolarized. 4. **Postsynaptic Current:** - The nonspecific current (`i`), calculated as the product of conductance (`g`) and membrane potential difference from the reversal potential (`e`), represents the ionic currents through the receptor channel. This aligns with how NMDA receptor activation leads to cation influx, contributing to excitatory postsynaptic potentials (EPSPs). 5. **Synaptic Plasticity and Integration:** - While not explicitly detailed in the code, NMDA receptors support synaptic plasticity processes (like long-term potentiation, LTP) due to their calcium permeability, which acts as a secondary messenger in synaptic signaling pathways. Thus, models like this provide foundational components for larger models investigating synaptic integration and plasticity. ### Summary In summary, this code models a summating form of NMDA receptor-mediated synaptic transmission, highlighting characteristic features such as dual-exponential conductance kinetics, voltage-dependent magnesium block, and the resulting ionic currents. These features are central to understanding synaptic integration and plasticity in neural networks.