The provided code models a graded synapse with first-order binding kinetics, specifically focusing on an excitatory synapse, likely mediated by AMPA-type glutamate receptors. Here is a breakdown of the biological basis that directly relates to the code:

Biological Basis:

1. Graded Synapse:

   • Unlike traditional synaptic models that involve a sharp action potential threshold for neurotransmitter release, graded synapses can convey information via subthreshold voltage changes. This is often the case in systems where neurotransmitter release is modulated by varying membrane potentials, such as in certain retinal and sensory neurons.

2. Neurotransmitter Binding Kinetics:

   • The model involves first-order binding kinetics, a simplification where the rate of neurotransmitter binding and unbinding to its receptor determines the synaptic conductance changes. This is captured by the 's' (state) variable, which represents the synaptic gating based on neurotransmitter availability.

3. Excitatory Synapse:

   • The parameter e = -70 mV indicates the reversal potential, suggesting a synapse that is excitatory. Excitatory synapses often involve AMPA receptors that permeate sodium (Na+) and potassium (K+) ions, leading to depolarization of the postsynaptic cell.

4. Voltage-Dependence:

   • The presynaptic voltage (V_pre) influences the state (s_inf) of the synapse. The threshold (V_thr) and slope (V_slope) parameters define how sensitive neurotransmitter release is to changes in membrane potential, reflecting the synapse's intrinsic properties.

5. Maximal Conductance:

   • The g_max parameter represents the maximal conductance of the dAMPA (decayed AMPA receptor), akin to the maximal number of receptor channels available for ion passage upon full activation by neurotransmitters.

6. Conductance-Based Synaptic Current:

   • The code calculates the synaptic current (i) as a product of conductance (g) and the driving force (the difference between the postsynaptic membrane potential and the reversal potential), common in excitatory synapse models involving AMPA receptors.

Key Features:

• Gating Variable (s): Represents the fraction of open synaptic receptor channels influenced by neurotransmitter binding. Its dynamics are governed by the difference between its steady-state value (s_inf) and its current value, scaling with the kinetic parameter tau, reflecting synaptic plasticity and desensitization.

• Steady-State Activation (s_inf): This is determined by a hyperbolic tangent function, indicative of a continuous and graded response to presynaptic membrane potential (V_pre), which directly ties to the nature of graded synaptic transmission.

The model's focus on graded synaptic transmission and voltage-dependent conductance changes mirrors the complexities found in certain neuronal systems, emphasizing the nuanced control of synaptic efficacy beyond traditional all-or-nothing mechanisms.