# Biological Basis of the AMPA Receptor Model with Pre-synaptic Short-term Plasticity This code models the dynamics of an AMPA-type glutamate receptor, incorporating mechanisms of pre-synaptic short-term plasticity (STP), as described by Fuhrmann et al., 2002. The model captures two essential phenomena: the synaptic current generated by AMPA receptors and the modulation of synaptic strength through pre-synaptic STP. ## AMPA Receptors AMPA receptors are a subtype of ionotropic glutamate receptors that mediate fast excitatory synaptic transmission in the central nervous system. When glutamate binds to AMPA receptors, they allow the flow of cations, primarily sodium (Na⁺) and to a lesser extent calcium (Ca²⁺), into the post-synaptic neuron, leading to depolarization and the generation of an excitatory post-synaptic potential (EPSP). - **Conductance Profile**: The code uses a dual-exponential function to model the time course of AMPA receptor activation and deactivation. This is physiologically relevant as it captures the rapid rise and slower decay characteristic of AMPA receptor-mediated currents in response to synaptic stimulation. ## Pre-synaptic Short-term Plasticity (STP) STP refers to the transient changes in synaptic strength due to the history of synaptic activity. It consists of facilitation and depression, mechanisms that adjust synaptic efficacy over short time scales (milliseconds to seconds). - **Facilitation and Depression**: The parameters `U1`, `tau_rec`, and `tau_fac` represent the STP characteristics. - **`U1`**: The baseline utilization of available synaptic resources upon stimulation, analogous to the probability of neurotransmitter release. - **`tau_rec`**: The time constant for recovery from synaptic depression, reflecting the replenishment rate of readily releasable vesicles. - **`tau_fac`**: The time constant for facilitation, representing the decay of residual calcium that transiently increases the probability of neurotransmitter release. - **Depression Mechanism**: Once a neurotransmitter is released, the probability (`P`) decreases due to vesicle depletion and gradually recovers (`tau_rec`). - **Facilitation Mechanism**: Previous activity increases `Use`, a factor reflecting the enhanced release probability caused by residual calcium, which decays over time (`tau_fac`). ## Model Functionality - **Reversal Potential (`e`)**: Set to 0.0 mV, which is typical for AMPA receptors reflecting the non-selective cation permeability. - **Synaptic Transmission**: Upon receiving a synaptic event (glutamate release), the model adjusts the conductance (`g`) and calculates the synaptic current (`i`) based on the driving force determined by the membrane potential (`v`) and the reversal potential (`e`). - **Dual-exponential Profile**: State variables `A` and `B` are used to calculate the conductance profile, accurately representing the temporal dynamics of AMPA receptor currents. The model integrates both synaptic receptor dynamics and STP to replicate realistic synaptic transmission influenced by immediate past activity, providing a detailed representation of synaptic processing at excitatory synapses.