The provided code is a simulation of a computational neuroscience model designed to explore the dynamics of neuronal networks, specifically within the context of subthalamic nucleus (STN) and globus pallidus (GP) interactions. This model seeks to capture the electrophysiological properties and synaptic interactions of neurons in these brain regions, which are crucial for understanding motion control and motor-related disorders, like Parkinson's disease. ### Biological Basis: 1. **Subthalamic Nucleus (STN) Neurons:** - **Ionic Currents:** - *Sodium (\(I_{Na}\)), Potassium (\(I_K\)), and Calcium (\(I_{Ca}\))*: These are fundamental ionic currents that contribute to the action potential generation and overall excitability of neurons. The model includes detailed descriptions of these currents via parameters like conductance (\(g_{Na}\), \(g_K\), etc.) and reversal potentials (\(V_{Na}\), \(V_K\)). - *AHP Currents (\(I_{AHP}\))*: Afterhyperpolarization currents, mediated by calcium-activated potassium channels, are modeled to represent post-spike behaviors influencing firing rates. - *Ionic Conductance and Gating Variables:* These include state-dependent activation and inactivation properties (\(m\), \(h\), \(n\), etc.), which are modeled with equations defining \(m_{\text{inf}}, h_{\text{inf}}\), etc., based on membrane potential. 2. **Synaptic Interactions:** - *Chemical Synapses (\(I_{\text{syn}}\))*: These interactions are modeled to replicate the connections between STN neurons. Parameters like synaptic weight (\(g_{\text{syn}}\)) and reversal potential (\(V_{\text{syn}}\)) dictate the strength and polarity of synaptic signaling. - *Delayed Interactions:* Relay synaptic transmission dynamics, which are represented through delay functions within the code, reflecting realistic synaptic delay effects. 3. **Stimulation Protocol:** - The model includes external stimulation, with parameters like frequency (\(fr\)) and current strength (\(I_{\text{stim}}\)), designed to simulate external inputs such as those from other parts of the brain or experimental stimulation protocols. - **Local and Non-local Spread:** The parameters \(w1\) and \(w2\) reflect the spatial distribution of the stimulation on the neuronal network, allowing simulation of both local and more diffuse stimulation scenarios. 4. **Globus Pallidus (GP) Neurons:** - Similar to STN neurons, GP neurons incorporate detailed ionic and synaptic current descriptions. - **Gating Variables and Currents:** As with STN, the GP model incorporates gating dynamics for sodium, potassium, and other relevant ionic channels. This helps simulate the specific firing patterns and responses of GP neurons to external inputs. 5. **Population Dynamics and LFP:** - The model simulates the local field potential (LFP) as a proxy for the collective synaptic and spiking activity, calculated using synaptic currents at a specific location. LFP can be an important measure for comparing model predictions against potential electrophysiological recordings. ### Conclusion: The model provides a comprehensive simulation environment to analyze the biophysics and connectivity of STN and GP neurons, critical components of basal ganglia networks. These models help in understanding the mechanisms of motor control, decision making, and the pathophysiology of movement disorders, offering insights into therapeutic interventions, like deep brain stimulation and pharmacotherapy.