# Biological Basis of the Computational Model The provided code is an implementation of a cellular automaton model that simulates neuronal firing dynamics within a network. This model draws on key biological principles to replicate aspects of neuronal communication and behavior, particularly focusing on the process of neuronal firing and the influence of network connectivity. Here are the key biological aspects represented in the code: ## Neuronal Firing Dynamics ### Initial Conditions and States - The `cells` array symbolizes the initial state of neurons, where each cell represents a neuron that can be in three states: - **Firing (excited)**: A state when the neuron is actively transmitting signals, represented by a value of `1`. - **Refractory**: A period following excitation where the neuron cannot fire, represented by a negative value indicating progression through the refractory period. - **Resting**: A non-active state, represented by `0`, where the neuron is ready to fire upon stimulation. ### Refractory Period - The `t_r` parameter corresponds to the biological refractory period, a time during which a neuron cannot activate again immediately after firing. ### Stimulation and Randomness - The model integrates a randomness component in neuronal firing through a Poisson process governed by `lambda`. This mimics the probabilistic nature of synaptic input and spontaneous neuronal firing due to fluctuations in synaptic excitation and inherent noise in neural systems. - `stim` represents external stimulation events to mimic synaptic input from other neurons. These are likely excitatory inputs that can trigger the firing of neurons that are not inhibited by the refractory period. ## Network Structure and Connectivity ### Neuronal Connections - The variable `conn` defines the network connectivity, identifying neighboring neurons for each cell. Connectivity plays a crucial role in a neuron's ability to fire, aligning with the biological concept of synaptic networks where the connectivity and strength of synaptic inputs influence neuronal excitation. - The `n_conn` parameter sets a threshold for the number of connections, affecting a neuron's firing likelihood based on network interactions. It represents structural or functional connectivity restrictions found in neural circuits. ### Excitation Influenced by Neighbors - The sub-function `next_to_excited` checks adjacent neurons (neighbors) to determine whether a neuron can fire. Neurons require excitation from at least two neighbors or stimulation, which parallels biological rules governing synaptic integration where multiple inputs are necessary for reaching the threshold potential. ### Overlap in Activity - The `overlap` parameter depicts the duration over which a neuron is considered to exhibit activity after excitation. This can be likened to sustained depolarization phases or continued influence of neuromodulators causing a prolonged energetic state in neurons. ## Conclusion This model captures essential features of neuronal dynamics, such as the influence of local circuit connectivity, the stochastic nature of neural firing, and the refractory mechanism that modulates neuronal excitability. By abstracting these biological principles, it provides a simplified but meaningful representation of neuronal network dynamics suitable for computational studies, allowing exploration of how local interactions lead to emergent global behavior in neural systems.