# Biological Basis of The Code The provided code is a computational model based on the study by Kuznetsova and Deth (2007), designed to simulate neuronal dynamics in a network composed of ten cells: eight excitatory (E) cells and two inhibitory (I) cells. This is a simplified representation of a neurobiological system, focusing on the interactions between excitatory and inhibitory neurons. ## Key Biological Elements ### Neurons - **Excitatory Neurons (E cells)**: Represented by variables `Ve1` to `Ve8`. Each neuron is characterized by its membrane potential (voltage) and its interactions with other neurons through synaptic connections. - **Inhibitory Neurons (I cells)**: Represented by variables `Vi1` and `Vi2`. These neurons influence the excitability of the E cells, thereby modulating network activity. ### Ionic Channels - **Potassium Channels (K Channels)**: Represented by variables `Re` for E cells and `Ri` for I cells. The `R` gating variables follow a time constant, controlling the rate of channel opening and closing, which is crucial for neuron firing and repolarization. - **Calcium Channels (Ca Channels)**: Denoted by `Ce` for E cells and `Ci` for I cells. Calcium dynamics participate in various cellular processes, including neurotransmitter release and modulation of other ionic channels. - **Calcium-Dependent Potassium Channels (Ca-K Channels)**: Indicated by `He` for E cells. These channels are activated by intracellular calcium and influence the neuron's return to a resting state after an action potential. ### Synaptic Connections - **Synaptic Variables (`Fe`, `Se`, `Fi`, `Si`)**: These variables represent synaptic activities and are influenced by a step function (Heaviside function) based on the membrane potential relative to a threshold (`W`). These variables describe: - `Fe` and `Se` for excitatory synapses. - `Fi` and `Si` for inhibitory synapses. - **Synaptic Parameters**: - `GSee`: Conductance of excitatory to excitatory synapses. - `GSei`: Conductance of excitatory to inhibitory synapses. - `GSi`: Conductance from inhibitory cells. ### Membrane Potential Dynamics - **Equations**: The dynamics of each neuron (e.g., `Ve1'`, `Vi1'`) include terms for various ionic currents (`Minf`, `Re`, `Ce`, `He`) and synaptic inputs, capturing the complex interplay between ionic channel activity and synaptic inputs. - **Input Current (`Ie`)**: External current applied to E cells, modulating their firing rate. ### Activation Functions - **Steady-State Activation Functions**: - `Cinf`, `Minf`, and `Rinf`: Describe the activation curves for calcium, membrane, and potassium conductances, respectively, as functions of the membrane potential. ## Purpose of the Model The model aims to replicate neuronal population dynamics and investigate how neurons interact through synaptic connections and various ionic channels to produce network oscillations and patterns. Specific attention is given to the roles of different ionic channel dynamics and synaptic interactions in generating and regulating neuronal firing patterns. By simulating a network of interconnected excitatory and inhibitory neurons, the model provides insights into the underlying mechanisms of neuronal communication and processing, potentially reflecting biological phenomena observed in cortical and subcortical structures in the brain. This computational framework allows researchers to explore alterations in parameters, study the effects of different synaptic coupling strengths, and examine how these factors influence the emergent dynamics of the neural network, contributing to our understanding of similar processes in the living brain.