The code provided models the electrical activity of neurons using a modified version of the Morris-Lecar model, which is a well-known mathematical model used to simulate neuronal excitable cells and their action potentials. This particular model is modified following the work by Prescott (2008), which means it builds upon the original Morris-Lecar framework to include additional features or tweaks for specific experimental conditions or insights. Here are the key biological components represented in the model: ### Neuronal Excitability The code simulates neurons' electrical behavior by describing the dynamics of the membrane potential (V) and ion channel gating (y), which influence how neurons generate action potentials. ### Ionic Currents 1. **Fast Inward Current (\(I_{Na}\))**: - Simulated through an instantaneous activation mechanism represented by \(m_{inf}(V)\). - Modeled as a sodium (\(Na^+\)) current activating rapidly as the membrane potential changes. - This current is characterized by parameters such as maximal conductance (\(gna\)) and a reversal potential (\(vna\)), reflecting the properties of sodium channels. 2. **Delayed Rectifier Current (\(I_{Kdr}\))**: - Mediated by the gating variable \(y\), which changes more slowly than the sodium current activation. - Represents a potassium (\(K^+\)) current involved in repolarizing the membrane potential after an action potential. - Characterized by \(yinf(V)\), \(tauy(V)\), and associated maximal conductance (\(gk\)) and reversal potential (\(vk\)). 3. **Leak Current (\(I_l\))**: - Represents a passive flow of ions contributing to the resting membrane potential. - Characterized by a constant conductance (\(gl\)) and reversal potential (\(vl\)). ### Noise and Stimulus - **Noise**: The inclusion of noise terms (\(nd\) and \(dc\_noise\)) represents the stochastic nature of ion channel opening and closing, reflecting biological variability and randomness in neuronal firing. - **External Stimulus (\(I_{ext}\))**: The model incorporates an external stimulus, which can mimic the experimental conditions where neurons are subjected to external inputs. ### Simulation Details - **Time Dynamics**: The model uses differential equations for continuous dynamics, typical for capturing the time-dependent behavior of ion channels and membrane potentials in neurons. - **Neuronal Class**: The parameters such as \(beta_y\) and \(\gamma_y\) influence the class of neuronal excitability, affecting how the neuron responds to inputs based on parameter adjustments. This relates biologically to different classes of excitability (Type I, II, III) as observed in various neurons. This computational model is an abstraction of the biological processes that underlie neuronal excitability and synaptic integration, providing insight into how various ionic currents and external factors influence neuronal firing and signaling.