# Biological Basis of the Fluctuating Conductances Model The provided code models the impact of synaptic bombardment on a neuron's membrane potential using fluctuating synaptic conductances. Synaptic bombardment represents the effect of a large number of synaptic inputs a neuron receives, which is particularly important in recreating in vivo-like dynamics in computational models of neurons. ## Key Biological Concepts ### Synaptic Conductances - **Excitatory and Inhibitory Conductances:** The model simulates two types of synaptic conductances: - **Excitatory Conductance (g_e):** Associated with excitatory neurotransmitter activity, leading to depolarization of the neuron. It's commonly linked with excitatory synapses utilizing glutamate. - **Inhibitory Conductance (g_i):** Arises from inhibitory neurotransmitters, leading to hyperpolarization or stabilization of the neuron's membrane potential. It is often related to synapses that use GABA (Gamma-Aminobutyric Acid). ### Reversal Potentials - **E_e (Excitatory Reversal Potential):** Typically set around 0 mV, indicating excitatory synapses drive the membrane potential toward this value. - **E_i (Inhibitory Reversal Potential):** Set at -75 mV, typical for inhibitory synapses, meaning they drive the potential in the opposite direction. ### Stochastic Processes and Synaptic Variability - The model describes g_e and g_i as stochastic variables driven by Ornstein-Uhlenbeck processes, capturing the inherent variability and noise in biological synaptic input due to factors like neurotransmitter release variance and synaptic channel gating kinetics. ### Time Constants - **Tau_e and Tau_i:** Represent the temporal dynamics of the conductances, corresponding to biological processes such as the opening and closing kinetics of synaptic ion channels. In this case, tau_e (2.728 ms) would typically relate to excitatory synapses with fast dynamics, while tau_i (10.49 ms) aligns with slower dynamics typical of inhibitory synapses. ### Noise and Diffusion - **Noise (Ft):** Gaussian white noise models random fluctuations in synaptic input, reflecting the irregularity inherent in biological synapse functionality. - **Diffusion Coefficients (D_e and D_i):** Quantify the intensity of conductance fluctuations, directly influenced by the variance of input conductances, thus emerging from biological synaptic noise. ### Biological Implementation - **Non-specific Current:** The model calculates a composite current `I_syn`, representing the sum of excitatory and inhibitory synaptic currents, and impacts the neuron's voltage, mimicking realistic synaptic bombardment in neurons. By simulating synaptic bombardment through fluctuating conductances, this model aims to recreate the complexity and variability of real neuronal activity within computational frameworks, providing insights into neuronal dynamics under diverse synaptic conditions typical in the cerebral cortex.