The provided code represents a computational model of presynaptic short-term facilitation and depression, focusing specifically on the dynamics of calcium (Ca²⁺) and neurotransmitter release. This model is pertinent to understanding synaptic transmission processes that occur in the presynaptic neuron as a result of action potential-induced calcium influx.

Biological Basis of the Model

1. Calcium Dynamics:

   • The model considers the dynamics of bound calcium concentration, a critical component in synaptic transmission. Calcium ions play a pivotal role in neurotransmitter release at the synaptic cleft by acting as a signal for synaptic vesicle fusion with the presynaptic membrane.
   • The code calculates the bound calcium concentration using a first-order differential equation that accounts for the balance between calcium influx due to action potentials (represented by the calcium current input, u) and the intrinsic decay of calcium levels over time (TauCa).

2. Release Probability:

   • The probability of neurotransmitter release (Prel) is computed based on the fourth power of the calcium concentration, indicating a cooperative binding of calcium ions to sensor proteins in the presynaptic terminal. This non-linear relationship highlights calcium's essential role in facilitating synaptic release.

3. Vesicle Dynamics:

   • The model tracks the "releasable vesicle ratio" (Rrel), which represents the fraction of synaptic vesicles ready to release neurotransmitter. This variable is influenced by two processes: vesicle recovery through replenishment and vesicle depletion due to calcium-dependent release events.
   • The equation for Rrel considers both the recovery of depleted vesicles (krecov) and the depletion due to synaptic transmission events controlled by release probability (Prel) and calcium influx (u).

4. Neurotransmitter Release:

   • The final output of the model is the rate of neurotransmitter flux (dGlu/dt), representing the release of glutamate, a common excitatory neurotransmitter, from the presynaptic neuron into the synaptic cleft.

5. Parameters and Constants:

   • Ca0, KCa, krecov0, and Prelmax are fixed values determining baseline conditions for initial calcium concentration, binding dynamics, recovery kinetics, and maximum release probability, respectively. These parameters reflect established physiological properties of presynaptic terminals.

Context and Application

Overall, the model reflects the cellular mechanisms underpinning short-term synaptic plasticity. Short-term facilitation increases neurotransmitter release probability following repetitive stimuli due to residual calcium accumulation, whereas short-term depression results from the depletion of readily releasable vesicle pools. Models like this are critical for simulating and understanding the complex dynamics at synapses, which are fundamental to neural circuit function and information processing in the brain.