# Biological Basis of Fluctuating Conductance Model ## Overview The code provided represents a computational model of synaptic activity in neurons, specifically focusing on the stochastic nature of synaptic conductance. This model simulates the impact of synaptic bombardment, where neurons receive a barrage of excitatory and inhibitory inputs that fluctuate over time due to random variations, akin to what is observed in vivo. ## Key Biological Components ### Synaptic Inputs 1. **Excitatory Conductance (`g_e`)**: - Described by a fluctuating conductance driven by excitatory presynaptic neurons. - Aims to mimic the influence of neurotransmitters, such as glutamate, which open channels allowing Na+ and Ca2+ to enter and depolarize the neuron. - Features a reversal potential `E_e`, representing the equilibrium potential for excitatory ion flow, typically near 0 mV. 2. **Inhibitory Conductance (`g_i`)**: - Represents inhibitory synaptic inputs, conducted through neurotransmitters like GABA or glycine, which typically result in Cl- influx and neuron hyperpolarization. - Characterized by its reversal potential `E_i`, often set to -75 mV to mimic inhibitory post-synaptic potential equilibrium. ### Stochastic Processes - Synaptic conductances are represented using **Ornstein-Uhlenbeck (OU) processes**, a common way to simulate the temporal dynamics of noisy biological signals. - Conductance fluctuations happen due to random synaptic activity, modeled as Gaussian white noise (`Ft`), which captures the unpredictable nature of synaptic transmission. ### Biological Parameters - **Time Constants (`tau_e`, `tau_i`)**: - Represent the decay time of synaptic conductances, associated with the kinetics of synaptic channel closure after neurotransmitter unbinding. - **Noise Diffusion Coefficients (`D_e`, `D_i`)**: - Describe the magnitude of fluctuations, related to the variance of synaptic conductance, reflecting the variability of synaptic strength in real neurons. ## Model Equation The model simulates the synaptic current (`Isyn`): \[ Isyn = g_e(t) \times [V - E_e] + g_i(t) \times [V - E_i] \] Here, `V` is the membrane potential of the post-synaptic neuron. This equation represents the net effect of synaptic inputs on neuronal voltage, integrating excitatory and inhibitory influences in a dynamic balance. ## Significance This model provides a simplified yet biologically relevant depiction of synaptic conductance, allowing for the exploration of neuron dynamics under conditions resembling in-vivo synaptic bombardment. It is crucial for understanding neuronal response variability and network dynamics, as it reflects the impact of continuous synaptic input fluctuations similar to those occurring in a neuronal network in the brain.