The provided code models a synapse in a computational neuroscience context, specifically focusing on the NMDA (N-methyl-D-aspartate) receptor function. The NMDA receptor is a type of ionotropic glutamate receptor that plays a crucial role in synaptic plasticity, which is believed to underlie mechanisms of learning and memory in the brain.

Biological Basis

1. NMDA Receptor Dynamics:

   • The code models the dynamics of the NMDA receptor by defining two states: open (o) and closed (c). These states are indicative of the receptor being in an active (allowing ion flow) or inactive state.
   • The states evolve over time, modeled by exponential decay with time constants tau_o and tau_c, representing the open and closed state time constants, respectively. These values determine how quickly the NMDA receptor transitions between its states.

2. Voltage Dependence:

   • The NMDA receptor is both ligand-gated and voltage-dependent. The function mgBlock_std represents the voltage-dependent magnesium block, a hallmark feature of NMDA receptors. Under resting potential conditions, the receptor is blocked by Mg²⁺ ions, an effect which diminishes as the membrane depolarizes: [ mgBlock_std = \frac{1}{1 + c1 \cdot e^{c2 \cdot v}} ]
   • This equation models the relief of magnesium block as the membrane potential (v) becomes more depolarized, allowing cations such as Ca²⁺, Na⁺, and K⁺ to flow through the channel.

3. Synaptic Current:

   • The synaptic current (i) calculation includes factors such as the voltage (v), reversal potential (erev), and the state variables (o and c). The formula: [ i = mgBlock_std(v) \cdot (c - o) \cdot (v - erev) ] models the synaptic current as a function of the potential difference and the gating variables, modulated by the voltage-dependent magnesium block.

4. Stochasticity in Synaptic Transmission:

   • Variability in synaptic responses is introduced by using a random number generator (randGen) to simulate the stochastic nature of synaptic transmission. This reflects the biological variability observed in neurotransmitter release and receptor activation under physiological conditions.

5. Synaptic Weight:

   • The NET_RECEIVE block updates the synaptic states in response to presynaptic input, modulated by a synaptic weight (weight). The weight represents the influence or strength of the synapse, which can be a function of synaptic plasticity.

Overall, the code represents a simplified yet biologically plausible model of NMDA receptor dynamics, capturing the essential features of synaptic function and transmission, critical for understanding neural computation and plasticity.