The provided MATLAB function `inp_single_poisson` is designed to model a specific aspect of synaptic transmission in a neural network, specifically simulating synaptic input that can be described by a Poisson process. Here's a breakdown of the biological basis of the code: ### Biological Concept: Synaptic Transmission 1. **Excitatory Postsynaptic Potential (EPSP):** - The function is designed to generate a single input stream of EPSPs. EPSPs are depolarizing events caused by the influx of positively charged ions (typically Na⁺) into a neuron, making it more likely for the neuron to reach the threshold for firing an action potential. - EPSPs result from neurotransmitter release from presynaptic neurons, which bind to receptors on the postsynaptic cell and open ion channels. The function name suggests modeling these events. 2. **Poisson Process:** - In neuroscience, synaptic inputs are often modeled as stochastic processes, particularly Poisson processes. This is because synaptic inputs in neural systems arrive randomly in time, closely resembling the statistical properties of Poisson processes. - The function `inp_single_poisson` makes use of an auxiliary function `inp_poisson` to generate these stochastic input streams. This reflects the natural variability and randomness of synaptic transmission in biological neural systems. ### Parameters and Their Biological Relevance - **`N`:** Represents the number of events or the number of neurons from which the inputs are being accumulated. In a biological context, this might correspond to the number of presynaptic neurons connected to a postsynaptic neuron. - **`ts`:** Represents the time steps for the simulation, providing a temporal framework over which synaptic inputs are modeled. - **`I0` and `tau`:** While not used directly in this function, these parameters typically represent the amplitude and the decay time constant of EPSPs, respectively. The decay constant (`tau`) reflects how quickly the EPSP diminishes over time, which is essential for temporal dynamics in synaptic integration. - **`l` (lambda):** Likely reflects the rate parameter of the Poisson process, setting the expected frequency of synaptic events. In a biological system, this might correlate with the firing rate of presynaptic neurons. ### Summary The function `inp_single_poisson` uses a Poisson process to model the probabilistic arrival of EPSPs at a neuron, which is a fundamental characteristic of biological synapses under the influence of stochastic neurotransmitter release and synaptic transmission. This approach is crucial for understanding how neurons integrate synaptic noise to produce coherent neural activity and can be used to explore various computational properties, such as neural coding and network dynamics.