The code provided is a computational model representing cortical neural dynamics, focusing on interaction between two types of neurons: pyramidal neurons and inhibitory interneurons. Here's a breakdown of the biological basis embedded in the code: ### Biological Components 1. **Pyramidal Neurons (Py):** - **Role:** These are excitatory neurons primarily responsible for integrative functions and long-range connections within and across cortical areas. - **Modeling**: The dynamics of the pyramidal neuron population, `Py`, are governed by differential equations that consider inputs, recurrent connections, and modulation by inhibitory signals. 2. **Inhibitory Interneurons (Inh):** - **Role:** These neurons provide inhibition within the cortical network and play a crucial role in regulating the excitation-inhibition balance. - **Modeling**: The inhibitory neuron dynamics, `Inh`, are also governed by differential equations. They receive excitatory inputs from pyramidal neurons and modulate their activity through inhibitory connections. ### Dynamics and Mechanisms - **Synaptic Interactions:** - The model includes parameters for synaptic connectivity: `Py2Py`, `Inh2Py`, `Py2Inh`, `Inh2Inh`. These correspond to the strength of synaptic transmission between these neuronal populations. - Excitatory connections (e.g., `Py2Py`) are modeled where pyramidal neurons excite each other. - **Input Terms:** - **External Inputs:** `PyInput` and `InhInput` simulate external input to pyramidal and inhibitory neurons, respectively. This can represent thalamic input or other subcortical source influences. - **Noise (`NValue`)**: Adds randomness to mimic stochastic subcortical inputs affecting neural activity. - **Non-linear Activation (Sigmoid Function):** - The function `Sigm` represents a sigmoidal non-linear activation function often used to mimic the firing rate dynamics of neurons. It depends on parameters such as `SigThresh` (threshold) and `SigSteepness` (slope), which affect neural responsiveness and output firing rates. - **Time Constants:** - `tauPy` and `tauInh` represent the time constants of pyramidal and inhibitory neurons. These reflect how quickly neurons respond to inputs and reset after activity, an important aspect of temporal dynamics in neural processing. ### Computational Approach - **Euler Solver:** The choice of an Euler solver implies a simple and efficient numerical integration method for solving the model's differential equations, which approximate the continuous activity of neuronal populations over time. ### Conclusion This model is a simplified abstraction of cortical microcircuit dynamics, focusing on the interaction between excitatory pyramidal cells and inhibitory interneurons. It captures key processes such as synaptic connectivity, stochastic input influence, and non-linear response properties, providing insights into how cortical activity might be coordinated and regulated at a population level in the brain.