The code provided is a computational model simulating a simple neural network involving pyramidal cells (excitatory neurons) and interneurons (inhibitory neurons). This model aims to capture some key aspects of neuronal dynamics, synaptic transmission, and network rhythms typical of cortical circuits in the brain. Here is a breakdown of the biological basis behind the key parts of the code: ### Neuronal Modeling - **Pyramidal Cells**: These are modeled with properties like resting potential (\(V_{\text{resting}} = -70 \, \text{mV}\)), threshold potential (\(V_{\theta} = -52 \, \text{mV}\)), and reset potential (\(V_{\text{reset}} = -62 \, \text{mV}\)). Membrane capacitance (\(C_p\)) and leak conductance (\(G_L\)) are also specified, which dictate how the cells integrate incoming signals and return to resting state. - **Interneurons**: These are similarly modeled but with different properties, reflecting their distinct physiological characteristics. Their resting (\(-65 \, \text{mV}\)), threshold, and reset potentials, along with modified leak conductance parameters, support their role in providing inhibitory control over network activity. ### Synaptic Transmission - **AMPA and GABA Receptors**: The model includes AMPA receptor-mediated excitatory post-synaptic potentials (EPSPs) with associated parameters such as reversal potential (\(E_{\text{AMPA}} = 0\)) and decay constant (\(\tau_{\text{AMPA}} = 5 \, \text{ms}\)). GABA receptor-mediated inhibitory post-synaptic potentials (IPSPs) are parameterized similarly with a reversal potential (\(E_{\text{GABA}} = -80 \, \text{mV}\)). - **Connection Strengths**: Synaptic connections between neurons are parameterized by conductance values (e.g., \(G_{pp}\) for pyramidal-to-pyramidal connections) and a connection rate that probabilistically determines connectivity. ### Neural Firing and Plasticity - **Adaptive Dynamics**: The model incorporates an activity-dependent plasticity component through calcium dynamics (\(Ca[n]\)) and activity-dependent potassium conductance (\(P_{\text{ADP}}[n]\)), which are crucial for long-term plasticity and adaptation in real neurons. - **Stochastic Inputs**: The code simulates noise through random fluctuations in synaptic inputs (\(G_{\text{excitation}}\) and \(G_{\text{inhibition}}\)), mimicking the variability observed in biological neural firing due to spontaneous synaptic release or background neuronal activity. ### Network Dynamics - **Recurrent Connectivity**: The model implements recurrent excitation among pyramidal neurons and inhibition through interneurons. This setup can support synchronous activity and generate network oscillations, which are fundamental for various cognitive functions like attention and memory. - **Temporal Dynamics and Inhibitory Control**: Temporal control is given through parameters like refractory periods and input on/off timing. These reflect how neurons temporally integrate inputs and respond to sustained or transient changes in synaptic activity. ### Biological Relevance The model described in the code aims to replicate certain properties of cortical neural networks, specifically focusing on interplays between excitation and inhibition and their role in generating rhythmic activity. The pyramidal-interneuron network (PIN) model can be a core motif underpinning dynamics in cortical areas involved in attention, sensory processing, and cognition. By adjusting the parameters, researchers can explore how different biophysical properties and connectivity schemes affect neural dynamics, thereby providing insights into healthy and pathological brain functions.