The provided code is a computational model representing synaptic conductance fluctuations in neurons, specifically designed to simulate synaptic bombardment. This model is inspired by the biological process where neurons receive continuous, stochastic synaptic inputs from excitatory and inhibitory presynaptic neurons. These inputs lead to fluctuating conductances in the postsynaptic neuron, which in turn affect its membrane potential and firing behavior. ### Biological Basis 1. **Synaptic Conductances**: - **Excitatory Conductance** (`g_e`): Corresponds to the synaptic effect of excitatory neurotransmitters such as glutamate. The reversal potential (`E_e`) is set at 0 mV, indicative of EPSPs (Excitatory PostSynaptic Potentials) typically depolarizing the neuron. - **Inhibitory Conductance** (`g_i`): Corresponds to the inhibitory inputs, commonly mediated by neurotransmitters like GABA. The reversal potential (`E_i`) is -75 mV, reflecting IPSPs (Inhibitory PostSynaptic Potentials) that usually hyperpolarize the neuron. 2. **Mean and Variability**: - Both excitatory (`g_e0`, `std_e`) and inhibitory (`g_i0`, `std_i`) conductances are defined by their mean and standard deviation, capturing the average level and variability in synaptic input, respectively. This reflects the randomness and dynamic nature of synaptic transmission in neural circuits. 3. **Temporal Dynamics**: - **Time Constants** (`tau_e`, `tau_i`): These parameters represent the decay time of synaptic conductances. They dictate how quickly the conductances return to their baseline levels after being perturbed by synaptic input, analogous to the post-synaptic membrane return to baseline after a synaptic event. 4. **Diffusion Coefficients**: - The model incorporates diffusion coefficients (`D_e`, `D_i`) for excitatory and inhibitory conductances, aligning with the stochastic nature of synaptic transmission where synaptic inputs cause a continuous, random walk-like fluctuation in conductance. 5. **Random Fluctuations**: - The use of random number generation is crucial to simulate the stochastic aspect of synaptic bombardment. The biological justification is that synaptic release events (neurotransmitter release from synaptic vesicles) are inherently probabilistic. ### Modeling Objectives This model aims to capture the dynamic and stochastic nature of synaptic inputs influencing neuron behavior. By focusing on fluctuating conductances, it provides insights into how variations in synaptic input can modulate neuronal excitability and firing patterns. This is important for understanding neuronal processing in conditions of high synaptic activity, such as during sensory processing, wakefulness, or pathophysiological conditions like epilepsy. Overall, the model seeks to offer a simplified yet biologically plausible description of the continuous input neurons receive, representing a fundamental aspect of neural computation in the brain.