Biological Basis of the LUTsyn NMDA Synapse Model

The provided code models the NMDA receptor-mediated synaptic transmission within a computational neuroscience framework. Here, we explore the biological foundations underlying this model:

NMDA Receptors

NMDA (N-methyl-D-aspartate) receptors are a type of ionotropic glutamate receptor that plays a critical role in synaptic plasticity, learning, and memory. They are unique among glutamate receptors because of their voltage-dependent magnesium (Mg²⁺) block and their requirement for both ligand (glutamate) binding and postsynaptic depolarization to become fully activated.

Key Biological Features Modeled

1. Conductance and Ion Flow:

   • NMDA receptors are permeable to calcium (Ca²⁺), sodium (Na⁺), and potassium (K⁺) ions. The code models the conductance (g) through these channels, which translates to a postsynaptic current (i).
   • The conductance is modulated by the presence of the magnesium block (open_Mg). The block is relieved by depolarization of the membrane potential (v), as reflected by the exponential terms involving v in the calculation of open_Mg.

2. Voltage Dependence and Mg²⁺ Block:

   • NMDA receptors are known for their voltage-sensitive gate due to the Mg²⁺ block. This is captured in the code by the expression: open_Mg = (open) / (1 + exp(-62 * v * 0.001) * Mg / 3.57), representing how Mg²⁺ impairs ion flow through the receptor at hyperpolarized potentials.

3. Temporal Dynamics of Synaptic Input:

   • The model calculates inter-pulse intervals (tau1, tau2, tau3, tau4) to simulate the response to trains of synaptic inputs. This reflects the importance of synaptic timing on receptor activation and synaptic strength, as rapid sequences of spikes can lead to more receptor opening.

4. Synaptic Plasticity and Gain Modulation:

   • The gain parameter represents synaptic strength adjustments in response to recent activity patterns, thus modeling synaptic plasticity. Changes in gain are driven by a look-up table (gain_array), connecting past synaptic events to current synaptic efficacy.

5. Triple Exponential Model:

   • This mechanism (with components C, B, E) represents the complex kinetics of NMDA receptor activation and deactivation, capturing the receptor's slow kinetics and prolonged conductance changes.

6. Order of Spike Influence:

   • The order parameter categorizes the synaptic input based on the timing of spikes, mirroring how varying sequences can differently affect NMDA receptor activation, a biological detail important for encoding synaptic memory in neuronal circuits.

By incorporating these elements, the model provides a detailed computational account of NMDA receptor function, capturing its biophysical and temporal properties critical for understanding synaptic integration and plasticity in networks of neurons.