## Biological Basis of the Code The provided code is a computational model for simulating the electrical activity of a small network of neurons, focusing on the dynamics of ion channels and synapses. It uses a Hodgkin-Huxley type formalism to capture the essentials of neuronal excitability and synaptic interactions. Here are the key biological elements represented in the code: ### Neuronal Model 1. **Voltage Dynamics**: The code models the membrane potential \( V \) of each neuron, which is fundamental in generating action potentials. The dynamics are influenced by ionic currents through various channels. 2. **Ionic Currents**: - **Sodium (\( \text{Na}^+ \)) Current**: Formulated using gating variables \( m \) and \( h \) which represent the activation and inactivation states of Na\(^+\) channels, respectively. This is crucial for the rapid depolarization phase of action potentials. - **Potassium (\( \text{K}^+ \)) Current**: Modeled with the gating variable \( n \), it allows for the repolarization of the neuron following an action potential. - **Calcium (\( \text{Ca}^{2+} \)) Current**: Calcium currents, characterized by a separate conductance, influence various cellular processes, including neurotransmitter release. - **Leaky Current**: Represented by \( I_{\text{leak}} \), this current accounts for passive ion flow across the membrane. 3. **Calcium Dynamics**: The concentration of intracellular calcium \( Ca \) is also modeled, which can affect other channel dynamics such as the afterhyperpolarization (AHP) current mediated by calcium-dependent potassium channels (\( g_{\text{ahp}} \)). ### Synaptic Interactions 1. **Synaptic Currents**: The neurons in the network communicate through inhibitory synaptic currents. The code uses variables like \( s \) to represent synaptic gating (analogous to neurotransmitter release probability), affecting postsynaptic potentials by opening synaptic channels. 2. **Synaptic Conductance**: The matrices \( G_i \) and \( G_e \) define the inhibitory and excitatory conductances, respectively, between neurons. In this model setup, \( G_i \) appears to be assigned significant values, suggesting a focus on inhibitory coupling between the neurons. ### Stimulation Protocol 1. **External Stimulation**: The model incorporates an external input current \( I_{\text{ext}} \) to simulate sensory or electrical stimulation, modulating the activity of neurons. This mimics the effect of sensory stimuli or experimental manipulations. ### Noise 1. **Stochastic Variation**: The term \( \text{noise\_int} \) introduces Gaussian noise into the membrane potential dynamics, representing biological variability and stochastic input from the network's environment or synaptic inputs. ### Modeling and Simulation 1. **Time Dynamics**: The integration is performed using a Runge-Kutta method (4th order), and the code is structured to simulate over two different time phases (possibly pre- and post-stimulation), denoted by \( N_{\text{step1}} \) and \( N_{\text{step2}} \). Overall, this code encapsulates major aspects of neuronal dynamics by simulating ion channel behaviors, synaptic interactions, and neural network connectivity, supported by key parameters derived from electrophysiological principles. It provides a biologically-inspired framework for understanding how neurons communicate within a network and respond to external stimuli.