# Biological Basis of the Code The provided code models the local connectivity of neurons in a cortical microcircuit using a Gaussian distribution. The biological basis of this model is rooted in the spatial organization and synaptic connectivity of neurons within the cerebral cortex, particularly concerning minicolumns or microcolumns. ## Key Biological Concepts ### Cortical Minicolumns - **Minicolumns** are the smallest structural and functional units of the cortex, comprising a vertical chain of neurons. Each minicolumn is typically associated with a range of 30-100 micrometers in diameter. - In this model, the term "minicolumns" is used as a reference for spatial scale, where a unit of 1 corresponds to 50 micrometers. ### Neuronal Connectivity - Neurons within the cortex exhibit local connectivity patterns which are essential for efficient information processing. These patterns often demonstrate a high degree of connectivity to nearby neurons, decreasing with distance. - The code models this local connectivity with a **Gaussian function**, where connectivity strength between neurons decays as a function of the distance between them. ### Gaussian Connectivity Model - The Gaussian function \( G(x) = \exp(-x^2/(2\sigmaG^2)) \) describes how the likelihood of synaptic connections decreases with distance, reflecting biologically observed local connectivity dynamics. - **Peak Synaptic Probability**: Closer neurons are more likely to be connected, showcasing the idea that neurons in proximity within a minicolumn are more likely to interact. - **Decay with Distance**: As distance increases, the probability of connections decreases, forming a bell-shaped curve typical of Gaussian distributions. ### Sparse Synaptic Matrix - The model uses a sparse matrix to represent the connectivity pattern. This reflects biological reality: despite a high potential for local connections, not all are realized. ### Distance Function - The code uses a distance function (`distfunc`) to compute the Euclidean distance in a 2D grid, simulating cortical surface topology where neurons are positioned. By incorporating these biologically inspired principles, the code aims to simulate and investigate the local connectivity dynamics within cortical circuits, reflecting the intricate balance between structure and function inherent in neuronal networks. These insights can be crucial for understanding various cognitive processes and disorders that involve cortical dysfunction.