## Biological Basis of the Model The code presented is a simulation of a network of excitatory and inhibitory neurons using the Morris-Lecar (ML) model, a type of conductance-based model that describes neuronal dynamics. ### Neurons and Synaptic Dynamics - **Neural Population**: The simulation models a total of 3000 neurons split into excitatory (Ne) and inhibitory (Ni) populations. This reflects common cortical architectures where excitatory neurons outnumber inhibitory ones. - **Excitatory (E) and Inhibitory (I) Neurons**: Both types of neurons in this model are described by variations of the Morris-Lecar model, which is a reduced model derived from Hodgkin-Huxley-type equations. This model incorporates voltage-gated ion channels that are critical for action potential generation. ### Ionic Currents and Gating Variables - **Membrane Potentials**: Voltages for excitatory and inhibitory neurons change over time based on a set of differential equations. The model uses reversal potentials (e.g., vnae, vke, vle) assigned to different ionic species: - **Potassium (K\(^+\))**: Represented by `gke` and `gki` conductances and their reversal potentials (`vke`, `vki`), key to neuron repolarization. - **Sodium (Na\(^+\))**: Represented by `gnae` and `gnai` conductances, important for depolarization and action potential propagation. - **Leak Currents**: Consist of `gle` and `gli`, accounting for passive membrane permeability. - **Gating Variables**: - `minf` and `winf` describe the activation and inactivation of ionic channels based on voltage, using sigmoidal functions (`tanh`). - `tauw` represents the timescale of gating variable recovery. ### Synaptic Interactions - **Synaptic Reversal Potentials and Conductances**: The `ve` and `vi` values represent the excitatory and inhibitory synaptic reversal potentials, crucial for synaptic current flow when neurotransmitters bind to receptor channels. - **Synaptic Weighting and Sparseness**: The model incorporates `Jee`, `Jie`, `Jei`, and `Jii`, representing the strength of synaptic connections between neuron groups. The network sparseness (`p`) is a probabilistic parameter describing how densely neurons are interconnected, which mimics the connectivity pattern in real neural circuits. ### External Inputs and Network Dynamics - **External Input**: External inputs modeled as Poisson spike trains (`inpute`, `inputi`) simulate random presynaptic spikes affecting the excitatory and inhibitory network components, mimicking sensory or intrinsic neural noise. ### Overall Goals - **Key Simulation Parameters**: The primary focus is on how variations in potassium reversal potential (`Ek_list`) affect dynamics such as neuronal firing rates. Potassium channels and their reversal potentials are pivotal in shaping the excitability and firing patterns of neurons. - **Network Dynamics**: The simulation aims to explore how changes in one parameter (potassium reversal potential in this case) influence the overall activity of a network, providing insights into the stability of excitatory and inhibitory balance, and their response to external inputs. Such aspects are critical for understanding phenomena like frequency responses, synchronization, and homeostatic regulation in neural circuits. By simulating these dynamics, the model seeks insights into realistic neural behavior potentially observed in biological systems under various neuromodulatory conditions, thus bridging computational neuroscience with experimental observations.