# Biological Basis of the Fluctuating Conductance Model ## Overview The provided code implements a model of synaptic bombardment using fluctuating conductances to simulate synaptic noise. The code models two primary types of synaptic input: excitatory and inhibitory, which are critical in shaping the electrical activity patterns of neurons in the brain. This model is biologically inspired and aims to reflect the conditions neurons experience in vivo, where they are influenced by continuous and variable synaptic inputs from other neurons. ## Biological Components ### Synaptic Conductance - **Excitatory and Inhibitory Conductances**: - **Excitatory Conductance (`g_e`)**: Simulates the increase in conductance when excitatory neurotransmitters bind to their receptors. This typically results in depolarization of the neuron, making it more likely to fire an action potential. - **Inhibitory Conductance (`g_i`)**: Represents the increase in conductance when inhibitory neurotransmitters bind to their receptors, usually resulting in hyperpolarization, thus decreasing the likelihood of the neuron firing. The reversal potentials for excitatory (`E_e` = 0 mV) and inhibitory (`E_i` = -75 mV) conductances are set to typical physiological values for these types of synaptic events. ### Stochastic Processes - The code uses the **Ornstein-Uhlenbeck (OU) process** to model the fluctuating synaptic conductances. This process mimics the random nature of synaptic release in a realistic way, incorporating both a deterministic mean and a stochastic component characterized by Gaussian white noise. - Parameters like correlation time (`tau_e`, `tau_i`) represent how long the memory of past states affects the present state of the conductance, reflecting the temporal dynamics of synaptic input variability. ### Variability and Noise - **Standard Deviations (`std_e`, `std_i`)**: These parameters represent the natural variability in synaptic conductances due to synaptic noise. It simultaneously models both the randomness in synaptic release and the intrinsic variability in synaptic response. - **Diffusion Coefficients (`D_e`, `D_i`)**: Calculated from the standard deviations and time constants, these coefficients quantify the strength of the noise applied to the conductances. ### Physiological Relevance - In vivo, neurons are subject to a constant bombardment of synaptic inputs, leading to fluctuating synaptic conductances. These fluctuations are not merely noise; they capture the essential dynamic by which neurons integrate synaptic inputs to generate a coherent output. - This model's purpose is to capture the statistical properties of synaptic input conditions in the brain, as described by Destexhe et al. (2001), to recreate the complex, irregular firing patterns observed in neurons in a controlled, simulated environment. ## Conclusion This model serves as a sophisticated representation of neuronal input dynamics, aiming to capture the essence of synaptic noise in the brain's neocortical neurons. By modeling excitatory and inhibitory synaptic bombardment as stochastic processes, it reflects the biological reality that neurons operate under a constant, fluctuating barrage of synaptic inputs contributing to their activity patterns.