## Biological Basis of the Code The provided code represents a computational model designed to simulate neuronal network dynamics with a focus on clusters of neurons. The biological basis of this model can be understood by exploring the biological concepts the code's parameters and structure aim to emulate. ### Clusters and Neuron Types 1. **Clusters of Neurons**: - The model's structure is based on clusters of neurons (`Nc` denotes the number of clusters), reflecting biological neural networks where neurons are often organized into such clusters. Each cluster in the model contains a defined number of neurons (`nn`). 2. **Types of Neurons**: - **Projection Neurons**: These neurons send signals to other clusters. In biological systems, they could represent pyramidal neurons, which are primarily excitatory and known for sending long-range connections. - **Interneurons**: These are local neurons within each cluster (specified by the probability `C` of connections within the cluster), typically inhibitory, to maintain balance in neural circuits. In the model, interneurons are primarily inhibitory as indicated by `Ii = 1`. 3. **Inhibitory and Excitatory Dynamics**: - `Ip` and `Ii` describe the proportions of inhibitory neurons among projection neurons and interneurons, respectively. This is reflective of the diverse functionality seen in the mammalian cortex, where inhibitory and excitatory neurons work together to regulate the timing and pattern of neural firing. ### Connectivity 1. **Inter-cluster Connectivity**: - `Pc` specifies the probability of connections between clusters. This simulates long-range inputs in biological neural networks, where neurons in different areas of the brain can influence each other. 2. **Spatial Connectivity**: - The power-law exponent `r` influences inter-cluster connectivity, echoing the heterogeneous connectivity patterns observed in the brain, where some neurons are more densely interconnected than others. ### Simulation and Dynamics 1. **Input and Response**: - External sensory inputs to the clusters are modeled (`S`), which could represent stimuli perceived by an organism and processed in various brain regions. 2. **Weight Matrix**: - `W` represents the synaptic weight, determining the strength of connections, a crucial factor in neuronal plasticity and information processing. 3. **Activation and Thresholds**: - Neurons' firing thresholds (`theta`) are set, determining the level of input required for neuronal activation, reflecting the concept of membrane potentials reaching a threshold to initiate action potentials in real neural systems. ### Additional Biological Considerations - **Dynamic Simulation**: - The model includes provisions for dynamic simulations over time steps (`max_steps`), allowing for the study of temporal evolution of neural activity, akin to observing neural responses over time in vivo. - **Stochastic Elements**: - Randomness (`seed`) in the simulation reflects the inherent variability and unpredictability in neural activity seen in biological systems. This computational model has been constructed to capture various aspects of neural network dynamics, focusing on clusters, connectivity, and neuron type interactions, which are key features of brain structure and function. The abstractions used are aimed at studying how these components collectively influence emergent properties such as information processing and network oscillations.