The code provided is a computational model of synaptic transmission at a hair cell synapse, specifically using an alpha function to describe the dynamics of synaptic activation. Hair cells are sensory receptors in the auditory and vestibular systems that convert mechanical stimuli into neural signals. The focus of this model is the synaptic connection between a hair cell and its postsynaptic target, simulating how neurotransmitter release affects postsynaptic current.

Biological Basis

1. Alpha Function Model:

   • The alpha function used in this model (alpha(t) = t/tau * exp(-t/tau)) represents the time course of synaptic conductance change typically observed in certain types of synapses. It characterizes the rise and exponential decay of the conductance, which mimics the transient nature of synaptic transmission following a presynaptic action potential.

2. Synaptic Conductance (g):

   • The state variable g represents synaptic conductance, which is modulated by the influx of ions through ionotropic receptors activated by neurotransmitter release. In hair cell synapses, calcium influx due to depolarization leads to neurotransmitter release, facilitating communication between sensory cells and neurons.

3. Time Constants (tau and atau):

   • tau characterizes the decay rate of the synaptic conductance, related to how quickly the synapse returns to its resting state after activation.
   • atau represents the time constant for synaptic activation rate, suggesting a stochastic process such as neurotransmitter release following a Poisson distribution, indicative of probabilistic events like vesicle release.

4. Delay and Synaptic Weight:

   • del (delay) refers to latency from presynaptic action potential to postsynaptic response, a crucial factor in rapid synapses such as the auditory ones.
   • sw (synaptic weight) dictates the strength of synaptic transmission, reflecting the effect of neurotransmitter release on postsynaptic current.

5. Neurotransmitter Release:

   • The stochastic modeling of activation rates and subsequent state transitions echo biological processes where neurotransmitter release probability and synaptic efficacy can vary due to factors like calcium concentration dynamics and vesicle availability.

Conclusion

This computational model captures key elements of synaptic transmission at hair cell synapses, emphasizing aspects of neurotransmitter release dynamics and postsynaptic conductance change. It provides a mechanism to simulate how sensory signals are encoded into neuronal signals, relevant for audition and balance. The use of an alpha function encapsulates the temporal profile of postsynaptic response to transient presynaptic events, reflecting the synaptic transmission's biological complexity.