The provided code models a graded synapse with first-order binding kinetics using a point process mechanism in the NEURON simulation environment. This type of synapse deviates from the classic all-or-nothing synaptic response and instead depicts a synapse where synaptic transmission is graded, meaning that the synaptic conductance can vary continuously as a function of the presynaptic membrane potential. Here's a detailed breakdown of the biological basis for the key components of the code:

Key Biological Concepts

1. Graded Synapse:

   • In traditional synapses, neurotransmitter release and postsynaptic response are typically all-or-none events. However, in some synapses, especially in certain types of neural circuits like those in the retina or between sensory neurons and interneurons in invertebrates, the transmission can be graded. This means that the synaptic conductance is a continuous function of the presynaptic membrane potential. The code models this by using a tanh function that smoothly varies s_inf, the steady-state gating variable, based on the presynaptic voltage (V_pre).

2. First-order Binding Kinetics:

   • This refers to the rate at which neurotransmitters bind to their receptors on the postsynaptic membrane being a simple exponential function of concentration. In the model, s represents the state variable for synaptic gating, akin to the fraction of bound receptors, and it evolves according to differential equations typical of first-order kinetics.

3. Synaptic Conductance (g) and Current (i):

   • The code calculates the synaptic current (i) using the conductance (g) and the difference between the postsynaptic membrane potential (v) and the synaptic reversal potential (e). The reversal potential (e = -70 mV) could correspond to that of chloride ions, considering excitatory conditions that may hyperpolarize under certain circumstances.

4. Maximal Conductance (g_max):

   • This parameter represents the peak conductance when the synaptic gating variable s is maximized. It is a key determinant of how strongly the synaptic potential can influence the postsynaptic cell.

5. Presynaptic Membrane Potential (V_pre):

   • The synaptic gating variable s_inf, which determines how much of the maximal conductance is achieved, is a function of the presynaptic voltage. This reflects the biological reality that neurotransmitter release (and thus synaptic response) is strongly dependent on the presynaptic neuron’s membrane potential.

6. Saturation (s):

   • The gating variable is constrained to biologically relevant limits (between 1e-06 and 1), ensuring the conductance stays within reasonable physiological bounds. This prevents unphysical behavior in the model.

7. Threshold (V_thr) and Slope (V_slope):

   • These parameters dictate the sensitivity of the synaptic response to changes in the presynaptic voltage, with V_thr representing the threshold above which significant synaptic effects start to occur, and V_slope defining the sharpness of the transition.

Conclusion

This code provides a model for simulating the dynamics of synaptic currents in response to graded changes in presynaptic voltage, a critical biological phenomenon in various neural circuits. The graded synaptic model serves to capture the nuanced behavior of certain synapses where the synaptic strength is a continuous function of presynaptic activity, offering insight into more complex neural computations than those seen in binary synaptic models.