# Biological Basis of the Code The code provided is intended to simulate the dynamics of a ring network model in computational neuroscience, specifically focusing on neuronal population activity using first-order rate models. Below is a summary of the biological elements and principles that this code captures: ## Key Biological Concepts 1. **Neuron Populations**: - The model considers two types of neuronal populations: excitatory and inhibitory neurons. - Biological systems have these two main types of neurons, with excitatory neurons typically using glutamate as a neurotransmitter to increase the likelihood of action potential firing in postsynaptic cells, and inhibitory neurons usually using GABA to decrease this likelihood. 2. **Ring Network Model**: - A ring network is a simplified model where neurons are arranged in a circular manner, allowing for lateral (side-to-side) interactions. - This setup is useful for exploring spatial aspects of cortical processing and sensory maps, akin to how visual and somatosensory cortices are organized. 3. **Lateral Connectivity**: - The model includes lateral interactions between neurons, capturing the notion that neurons connect not only to their immediate neighbors but also to more distant peers, with a specific decaying strength as distance increases (exponential decay). - This concept is biologically relevant because it reflects the fact that neurons in the brain are interconnected and can influence each other's activity over space. 4. **Transfer Function Formalism**: - Transfer functions in this context relate neuronal inputs to outputs, capturing the transformation of synaptic input into neuronal firing rates. - Such models are inspired by work by Amit & Brunel, Kuhn et al., and Zerlaut et al., and they reflect the synaptic integration properties of neurons, considering how synaptic inputs are converted into membrane voltage changes and subsequent spikes. 5. **Rate Models**: - The code implements a rate model derived from first-order approximations described by Wilson & Cowan (1970s) and El Boustani & Destexhe (2009). - These models abstract the firing rate of neuron populations without representing individual action potentials, which is important for understanding large-scale neural dynamics. 6. **Fixed Points and Dynamics**: - Fixed points are computed to understand stable states of network activity, which are likely candidates for operating points of neural circuits. - This reflects the idea that cortical systems often stabilize at certain levels of activity, a principle tied to homeostasis and efficient information processing. 7. **Stimulation Inputs**: - The code includes provisions for external stimuli affecting neuronal activity, mimicking how sensory input or experimental stimulation can influence brain dynamics. 8. **Euler Method for Numerical Simulation**: - The Euler method is used for numerical integration of the differential equations governing network dynamics, translating continuous-time models into a discretized format that allows for computational simulation. - The Euler method allows the model to simulate how neuronal dynamics evolve over time when exposed to various inputs and interactions. In summary, the provided code models the dynamic activity of interconnected neuronal populations in a simplified ring network, considering lateral connections, excitatory and inhibitory interactions, and the effect of external stimuli on these networks. These elements collectively encapsulate key biological principles underlying cortical networks, their connectivity, and their responsiveness to inputs, offering insights into neural computation and dynamics within the brain.