# Biological Basis of the Fluctuating Conductances Model The provided computational neuroscience code is an implementation of a model designed to simulate synaptic bombardment in neurons. This is represented by fluctuating synaptic conductances, capturing the inherent variability and randomness of synaptic input seen in biological neurons. ## Key Biological Components ### Synaptic Inputs Synaptic bombardment refers to the incessant activity occurring at synapses due to presynaptic action potentials causing neurotransmitter release, which in turn modulates post-synaptic conductance. This model features two types of synaptic inputs: excitatory and inhibitory. - **Excitatory Conductance (g_e):** Modeled with a reversal potential \( E_e = 0 \) mV. In biological neurons, this is typically mediated by synapses that release excitatory neurotransmitters such as glutamate, which open channels that allow cations like Na\(^+\) and Ca\(^2+\) to flow into the neuron. - **Inhibitory Conductance (g_i):** Modeled with a reversal potential \( E_i = -75 \) mV. This simulates the activity of inhibitory synapses, often mediated by neurotransmitters like GABA, which induce hyperpolarizing currents primarily through Cl\(^-\) influx. ### Conductance Fluctuations - The code models the synaptic conductances as stochastic processes using an Ornstein-Uhlenbeck process. These processes help introduce biologically realistic noise and variability, mimicking the unpredictable nature of real synaptic inputs in a neural environment. - **Diffusion Coefficients (D_e, D_i):** These are derived from the standard deviation of the conductances, reflecting how rapidly each conductance fluctuates around its mean, akin to the variability of synaptic release in biological systems. ### Time Constants (\(\tau_e, \tau_i\)) - These parameters represent the decay or correlation time of synaptic inputs. They capture the temporal dynamics of synaptic conductance changes, governing how long a conductance remains elevated after a synaptic event. Shorter \(\tau\) reflects a rapid, transient synaptic input (e.g., AMPA conductance), while longer \(\tau\) could represent slower, prolonged responses (e.g., NMDA or GABA receptor dynamics). ### Membrane Voltage (v) - The fluctuating current is calculated based on the membrane potential, which is a critical aspect of how synaptic inputs affect neuronal excitability and firing. By integrating over the current equations, the code attempts to capture the net effect of excitatory and inhibitory inputs on the membrane potential. ### White Noise (Ft) - The implementation uses Gaussian white noise to model the inherent randomness of synaptic transmission and the probabilistic nature of ion channel gating, fundamental to capturing realistic neuronal dynamics. ## Purpose The code aims to replicate the synaptic bombardment experienced by neocortical neurons in vivo. Such models are pivotal in understanding how synaptic variability contributes to neuronal computation and network dynamics, reflecting a more realistic neuronal environment involving constant and random synaptic activity. In summary, this computational model provides a framework to simulate the dynamic and stochastic nature of synaptic inputs and their effects on neuronal activity, elucidating the complex interplay of excitatory and inhibitory processes in the brain.