# Biological Basis of the Fluctuating Conductance Model The provided code models synaptic bombardment using fluctuating conductances to account for synaptic inputs to neurons. This model represents two key types of synaptic inputs: 1. **Excitatory Conductance (\(g_e(t)\))**: - This represents the synaptic conductance changes due to excitatory postsynaptic potentials (EPSPs), typically mediated by neurotransmitters like glutamate. - The reversal potential (\(E_e = 0 \, \text{mV}\)) indicates that excitatory inputs generally aim to depolarize the neuron toward this potential. 2. **Inhibitory Conductance (\(g_i(t)\))**: - This represents the synaptic conductance changes due to inhibitory postsynaptic potentials (IPSPs), generally mediated by neurotransmitters such as GABA. - The reversal potential (\(E_i = -75 \, \text{mV}\)) suggests that inhibitory inputs typically hyperpolarize the neuron toward this more negative potential. ## Fluctuating Conductance Model The model simulates synaptic bombardment by employing fluctuating conductances (\(g_e(t)\) and \(g_i(t)\)) described as Ornstein-Uhlenbeck (OU) processes. These processes enable the realistic modeling of synaptic input variability: - **Ornstein-Uhlenbeck Process**: - Both excitatory and inhibitory conductances are described by OU processes, which are stochastic processes that exhibit mean-reversion, making them suitable for modeling conductances that fluctuate around average values. - The model captures the temporal correlation inherent in synaptic activity through time constants (\(\tau_e\) and \(\tau_i\)), which indicate the decay of fluctuations toward their average. - **Noise and Variability**: - The model introduces a noise component to mimic the stochastic nature of synaptic inputs. This is achieved by introducing Gaussian white noise, scaled by diffusion coefficients \(D_e\) and \(D_i\). - These coefficients are calculated from the conductance variability (standard deviations \(\text{std}_e\) and \(\text{std}_i\)) and their respective time constants, linking noise directly to observed biological variability. ## Biological Parameters - **Average Conductances (\(g_e0\) and \(g_i0\))**: Represent the baseline levels of synaptic input conductance. - **Standard Deviations (\(\text{std}_e\) and \(\text{std}_i\))**: Reflect the variability or the extent of fluctuation in the synaptic conductance around its mean. - **Time Constants (\(\tau_e\) and \(\tau_i\))**: Indicate the temporal correlation or the persistence of fluctuations over time. ## Biological Implications This model provides a more realistic representation of synaptic dynamics by incorporating the probabilistic nature of synaptic transmission and the impact of synchronous neuronal input typically occurring in vivo. By using fluctuating conductances, the model is capable of simulating how neurons integrate excitatory and inhibitory inputs over time, contributing to the neuron's firing behavior and overall network dynamics. In summary, the code simulates more physiologically accurate neural behavior by accounting for the inherent noise and variability in synaptic inputs and their temporally correlated fluctuations, as seen in natural neural systems.