The provided code represents a computational model simulating the dynamics of a cortical column, a fundamental unit of computation within the brain. The model is particularly focused on the neural mass dynamics, which attempts to capture the collective behavior of neurons within a cortical column. This approach abstracts away individual neuron dynamics to focus on population-level characteristics, such as firing rates and synaptic interactions.
The code models two primary types of neuronal populations:
Pyramidal Neurons (Excitatory): These neurons are a major component of cortical columns, responsible for sending excitatory signals. The model captures their synaptic and intrinsic currents, particularly focusing on excitatory (AMPA receptor-mediated) and inhibitory (GABA receptor-mediated) synaptic inputs.
Inhibitory Interneurons: These neurons provide inhibitory regulation through GABAergic transmission, modulating the activity of pyramidal neurons.
The model incorporates both excitatory and inhibitory synaptic dynamics:
Excitatory Synapses (AMPA): These are mediated by AMPA receptors and contribute to the excitatory postsynaptic potential. The synaptic conductance (g_AMPA) and reversal potential (E_AMPA) determine the excitatory input strength and direction.
Inhibitory Synapses (GABA): These are mediated by GABA receptors, with conductance (g_GABA) and reversal potential (E_GABA) influencing the inhibitory postsynaptic potential.
The model includes several intrinsic currents which are vital for neuronal function:
Leak Currents: These stabilize the resting membrane potential of neurons, characterized by a leak conductance (g_L) and reversal potential (E_L).
Sodium-Dependent Potassium Current (I_KNa): An adaptive current influenced by sodium concentration, affecting neuronal excitability. The dynamics of this current play a crucial role in modulating neuronal firing and synaptic integration.
This represents the activity of ion pumps, particularly the Na⁺/K⁺ ATPase, crucial for maintaining ionic gradients across the neuronal membrane. This pump helps restore the resting potential following neuronal activity, and an imbalance here could affect signal transmission.
The model incorporates stochastic elements to account for biological noise and variability in neuronal responses. Random Gaussian noise is added to simulate the inherent unpredictability and variability observed in neuronal firing.
The model uses sigmoid functions to represent firing rates (get_Qp, get_Qi) of the neuronal populations, linking membrane potentials to firing probabilities. These nonlinear responses are crucial for capturing the threshold-driven spiking behavior observed in neurons.
Overall, the code constructs a simplified representation of a cortical column, focusing on the interaction between pyramidal and inhibitory neurons through synaptic dynamics, intrinsic membrane potentials, and adaptive currents. The inclusion of stochastic elements and various ionic currents aims to reflect the complex, dynamic environment of the brain, where intrinsic excitability and extrinsic stimuli converge to produce the rich behaviors seen in neural tissue. This type of modeling provides insights into physiological processes such as sleep regulation, as referenced in the header comments, and the underlying mechanisms of cortical processing.