# Biological Basis of the `PoissonTrigSyn.mod` Model The `PoissonTrigSyn.mod` model is designed to simulate an alpha function synaptic conductance, which represents synaptic current dynamics triggered by stochastic processes. Below is a detailed explanation of the biological concepts this code encapsulates: ## Synaptic Conductance In biological systems, synaptic transmission is a key mechanism for neurons to communicate. This involves the release of neurotransmitters from presynaptic neurons, binding to receptors on postsynaptic neurons, and consequently opening ion channels, leading to synaptic current. The model described here simulates: - **Alpha Function Conductance**: A mathematical representation of synaptic conductance where the conductance transiently increases to a peak before decaying exponentially. It is commonly used to model the time course of synaptic currents. The conductance (`g`) is described by: \[ g(t) = gmax \cdot \left(\frac{t - \text{onset}}{\tau}\right) \cdot \exp\left(\frac{-(t - \text{onset} - \tau)}{\tau}\right) \] This function peaks at `t = onset + tau`, aligning with synaptic response to presynaptic action potentials. ## Stochastic Synaptic Release - **Poisson Process**: The model introduces synaptic events based on a Poisson process. This reflects the probabilistic nature of neurotransmitter release, where synaptic vesicles are released at random intervals, often modeled as a Poisson event in computational neuroscience. - **Probabilistic Firing**: The synapse is triggered to release its conductance based on a probability (`prob`) and a generated pseudo-random number (`unitRand`). This approach mimics the stochastic firing of neurons due to random neurotransmitter release. ## Neural Parameters - **Firing and Refraction**: The model includes a `refraction` period to ensure that once a synaptic event is triggered, there is a refractory period where another synaptic event cannot immediately follow. This reflects the biological refractory period, during which a neuron is incapable of generating a second action potential. - **Membrane Potential and Current**: The `i` variable represents the synaptic current (`i = g * (v - e)`), where `v` is the membrane potential and `e` is the reversal potential. This mirrors the post-synaptic potential changes induced by synaptic currents in actual neurons. ## Randomness and Initial Seed - **Random Seed Generation**: The model uses a seed (`randseed`) for its random number generation, which ensures the reproducibility of the stochastic firing and synaptic events. In summary, the `PoissonTrigSyn.mod` file provides a simulated environment for synaptic conductance modulated by a stochastic process, capturing the essence of synaptic transmission variability and temporal dynamics in neuronal networks. This simulation contributes to understanding how neurons process and integrate temporally jittered synaptic inputs, reflecting real-biological neural communication intricacies.