# Biological Basis of the RING Model Code The provided code is designed to represent a computational model of neuronal connectivity, particularly in neural rings. This model, known as the RING model, captures aspects of synaptic connectivity and spatial organization of neurons. Below is a summary of the biological basis modeled by this code: ## Neuronal Network Structure The model simulates a one-dimensional neural ring, a configuration used to represent repetitive and cyclical neuronal interactions. This framework can be particularly relevant in capturing neuronal dynamics in structures such as the retina, cortical columns, and other circularly or symmetrically organized neural tissues. ## Parameters and Measurements ### Spatial Discretization - **X_discretization** and **X_extent**: These parameters define the spatial domain and resolution of the model, likely representing the physical arrangement of neurons in millimeters and discretized units (pixels). They are crucial for translating real-world distances into computational units. ### Connectivity Extents - **exc_connect_extent** and **inh_connect_extent**: These parameters define the extent of excitatory and inhibitory connections between neurons, measured in millimeters. They model how far the influence of a presynaptic neuron can extend within the network and contribute to the spatial spread of synaptic connections. ### Conduction Velocity - **conduction_velocity_mm_s**: This parameter depicts the speed at which action potentials propagate along axonal fibers. The normalized velocity parameter in the model is crucial for timing dynamics and neuronal signal transmission across spatial extents. ## Neuronal Dynamics ### Excitation and Inhibition The model differentiates between excitatory and inhibitory connections. Excitatory connections increase the likelihood of neuron firing, while inhibitory connections decrease it. The distinction serves to reflect the delicate balance between excitation and inhibition in the central nervous system, necessary for stable and adaptive network behavior. ### Gaussian Connectivity The `gaussian_connectivity` function models synaptic strength as a Gaussian distribution over space, with the peak (x0) representing the location of maximum synaptic strength, and the spread (dx) corresponding to the standard deviation of the distribution. This is a biologically realistic representation of synaptic connectivity, where proximal neurons have stronger synaptic connections, and connectivity weakens with distance. ## Biological Interpretation Overall, the code captures some fundamental aspects of neuronal networks, particularly how neurons influence each other through synaptic connections over a spatially organized structure. By utilizing Gaussian functions for modeling connectivity, the code mirrors the observed tendency of biological neuronal connections to have a spatial dependency with a peak influence and tapering effect over distance. This setup can be essential in understanding phenomena such as receptive fields, lateral inhibition, and spatial normalization within brain regions. In summary, the RING model code presented aims to abstract the spatial dynamics and connectivity principles underlying neuronal networks, focusing on structure, extent, and conduction velocity of signals within a simplified circular neuronal array.