The provided code models a synaptic conductance change in response to neurotransmitter release at a synapse, specifically capturing the kinetics of synaptic transmission. Here’s a breakdown of the biological basis:

Biological Basis

Synapse Model

• Two-State Kinetic Scheme: The model represents a synapse through a two-state kinetic process. In biological terms, this captures the transition of neurotransmitter-receptor binding and the subsequent conductance changes from this interaction.
• Rise and Decay: Synaptic conductance is described by two parameters: tau1 (rise time) and tau2 (decay time). In biology, these represent the time it takes for conductance to rise to its peak following a neurotransmitter release and the subsequent return to baseline, respectively. The condition tau2 > tau1 ensures the synaptic response peaks before decaying.

Conductance Dynamics

• Peak Normalization: The model normalizes the peak conductance to 1, meaning an event with weight 1 results in maximal conductance. This is akin to setting a standard unitary response in electrophysiological experiments.
• Coupled Exponential: The conductance is modeled as a sum of two decaying exponentials, capturing the precise timing of neurotransmitter release effects and their decay over a typical post-synaptic potential.

Noisy Dynamics

• Noise Term: The noise parameter introduces variability in the conductance dynamics. This captures the stochastic nature of synaptic transmission in biological synapses, where factors such as random neurotransmitter release and receptor binding contribute to variability in postsynaptic response.

SYNAPSE Types

• If tau2 approaches tau1, it approximates an alpha synapse, typified by a smoother, bell-shaped synaptic conductance profile.
• When tau1 is much smaller than tau2, it emulates a single exponential decay, resembling classic neurotransmitter receptor kinetics.

Biophysical Interpretation

• Receptor-Gated Conductance Change: The synaptic response is captured by non-specific conductances (g) that arise from ligand-gated ion channels opening upon neurotransmitter binding, leading to a post-synaptic current (i).
• Reversal Potential (e): Represents the equilibrium potential for the ion(s) flowing through the opened channels, analogous to reversal potentials set by specific ion gradients across the membrane.

Overall, the model seeks to replicate the dynamic processes underlying synaptic transmission, emphasizing timing (rise and decay), variability (noise), and normalization (peak conductivity).