The code you provided is simulating a network of spiking neurons using the Adaptive Exponential Integrate-and-Fire (AdEx) model, which is a biologically-inspired mathematical model often used in computational neuroscience to study neuronal dynamics. Let's break down the biological basis of this model and what this particular simulation is designed to achieve. ### Biological Basis 1. **Neurons and Their Properties**: - **The AdEx Model**: This model captures the basic excitability properties of neurons by simulating the membrane potential dynamics using an exponential integrate-and-fire mechanism. It includes adaptation properties that mimic real neuronal behavior, such as spike-frequency adaptation — a phenomenon observed in many cortical neurons. - **Parameters and Variables**: - Membrane capacitance (C), leak conductance (gl), resting potential (El), membrane potential threshold (vt0), and adaptation currents are parameters directly tied to neuronal biophysical characteristics. - The variable `V` is used to represent membrane voltage, while `w` represents adaptation current, which reflects ion channel activities (e.g., potassium currents involved in adaptation). 2. **Rheobase and Bifurcation Types**: - **Rheobase Current (Irheo)**: This is the minimum current amplitude of infinite duration required to evoke an action potential. It is a fundamental property associated with the excitability of neurons. - **Bifurcation Types**: The code distinguishes between different bifurcation types, specifically indicating Saddle Node or Hopf bifurcations. These terms describe how the neuron transitions from quiescent to spiking states and can provide insights into different firing patterns. The saddle node bifurcation is often associated with the type of excitability where a neuron can fire a spike upon the introduction of a small current. In contrast, a Hopf bifurcation can describe neurons with rhythmic activities. 3. **Network Dynamics**: - **Inhibition and Excitation Proportions**: The code iterates over varying proportions of excitatory and inhibitory neurons to observe the overall network activity. Biologically, this is important for studying how different balances of excitation and inhibition can affect overall brain states and dynamics. - **Spiking Frequency**: The simulated network's mean activity (number of spikes over time) is an output measure that reflects network excitability and states similar to those observed in real neural circuits. 4. **Simulation of Network Activity**: - By simulating a network of 50 neurons, this code attempts to model the collective dynamics of neurons subjected to different synaptic inputs (represented by current pulses) and how this affects their spiking activity. The inhibitory and excitatory interactions model the dynamic balance found in various biological neural circuits, particularly in cortical brain areas. ### Planned Experiments and Outputs - **Spike Raster and PSTH Plots**: These plots display when neurons fire, akin to recordings in neural experiments, and the peristimulus time histogram (PSTH) captures how often neurons fire over time. Such analyses are useful for understanding temporal patterns of neural firing in response to stimuli. - **Mean Activity Analysis**: Changes in mean neuronal firing rates as a function of inhibition proportion mirror studies in neuroscience that examine how varying levels of inhibition and excitation affect network function, potentially reflecting phenomena like altered states of consciousness or pathological conditions such as epilepsy. In summary, this code simulates a simplified neural network using models inspired by actual neuronal behavior and properties. It looks at how varying proportions of excitatory and inhibitory inputs can impact the overall activity of neurons, adding to our understanding of how these factors influence brain dynamics.