# Biological Basis of the Code The provided code is a computational model simulating small neural network dynamics using a leaky integrate-and-fire (LIF) neuronal model. The biological aspects of the model include the following: ## Neuronal Populations 1. **Excitatory Neurons (`Ecells`):** - The code defines a population of 2 excitatory neurons. - **Capacitance (`C`)**: Each excitatory neuron has a membrane capacitance of 15 µF for one and 14 µF for the other, reflecting their ability to store charge. - **Resting Potential (`VRest`)**: The resting membrane potential is set at -65 mV. - **Threshold Potential (`VThreshold`)**: The threshold for triggering an action potential is -66 mV. - **Reset Potential (`VReset`)**: After firing, the neuron's potential returns to -75 mV. - **Membrane Potential Variability**: The initial membrane potential is drawn from a normal distribution centered at -70 mV with a standard deviation of 3 mV. This introduces biological variability in neuron potentials. 2. **Inhibitory Neurons (`Icells`):** - Consists of a single inhibitory neuron. - **Capacitance**: The inhibitory cell has a capacitance of 10 µF. - **Resting Potential**: A resting membrane potential of -70 mV. - **Threshold Potential**: The neuron fires when reaching -66 mV. - **Reset Potential**: After firing, its potential resets to -80 mV. - **Membrane Potential Variability**: Similar to excitatory cells, the initial potential varies with a mean of -70 mV and a standard deviation of 4 mV. ## Synaptic Connectivity 1. **Excitatory Connections:** - Excitatory neurons connect to each other and the inhibitory neuron. - These connections are implemented with a "Delta" function, suggesting that when the presynaptic neuron fires, the postsynaptic potential is instantly altered. This instantaneous change is a simplification of synaptic transmission. 2. **Inhibitory Connections:** - The inhibitory neuron connects back to the excitatory neurons. - This connection is implemented as an "Exponential" synapse, which mathematically models the graded release and decrement of neurotransmitters over time, characterized by parameters: - **Time Constant (`Tau`)**: Set to 10 ms, indicating how quickly the inhibitory effect diminishes. - **Reversal Potential (`E`)**: -80 mV, which is typical for inhibitory postsynaptic potentials (IPSPs) mediated by the opening of Cl- or K+ channels. - **Conductance (`g`)**: A strength of 0.4 µS, reflecting the magnitude of conductance change upon neurotransmitter binding. ## Simulation Details - **Integration and Output**: The model simulates neuronal activity over 10 seconds in millisecond intervals. Membrane potentials and spike times are recorded, reflecting the biological interest in both sub-threshold dynamics and action potential firing. - **Environmental Variability**: There is a consideration of variability in potential changes through functions that add a stochastic delay to inhibitory transmission, modeling the variability that can emerge in neurotransmitter release and receptor interaction processes. Overall, the code models basic synaptic interactions within a simple network of neurons using their biophysical properties and synaptic relationships characteristic of real neural tissue, allowing for an exploration of network dynamics such as excitation, inhibition, and potential emergent properties within a controlled environment.