# Biological Basis of the Fluctuating Conductance Model The provided code models synaptic bombardment on neurons, designed to mimic the effect of synaptic input the neuron would receive in a biological system. This model reflects how neurons experience variability in synaptic conductances due to stochastic input from numerous synapses. ## Synaptic Bombardment ### Excitatory and Inhibitory Conductances 1. **Biological Relevance**: Neurons receive synaptic inputs that are either excitatory or inhibitory. Excitatory inputs, primarily mediated by neurotransmitters like glutamate, depolarize the neuron by increasing conductance to ions (e.g., Na⁺ and K⁺), making it more likely to fire. In contrast, inhibitory inputs, typically mediated by neurotransmitters like gamma-aminobutyric acid (GABA), hyperpolarize the neuron by increasing conductance to Cl^- or K⁺, reducing the likelihood of firing. 2. **Model Representation**: The parameters `g_e` and `g_i` in the code represent the conductances for excitatory and inhibitory synapses, respectively. These are modeled as stochastic Ornstein-Uhlenbeck processes, capturing the fluctuating nature of synaptic input due to the complex interplay of neurotransmitter release and receptor binding. ### Reversal Potentials - **Parameters `E_e` and `E_i`**: The reversal potentials for excitatory (`E_e`) and inhibitory (`E_i`) conductances are set to 0 mV and -75 mV, respectively. These values reflect the ion equilibrium potentials associated with excitatory (close to the Na⁺ equilibrium potential) and inhibitory inputs (GABA_A receptor channels, which are often permeable to Cl^- ions). ## Ornstein-Uhlenbeck Process - **Biological Justification**: Fluctuations in synaptic input are captured using an Ornstein-Uhlenbeck process, a mathematical model for the temporal evolution of a variable subject to both deterministic trends (mean reversion) and stochastic noise. Biologically, this reflects the flickering nature of synaptic inputs due to both changes in presynaptic activity patterns and intrinsic noise in synapse function. - **Parameters `g_e0`, `g_i0`, `std_e`, `std_i`, `tau_e`, and `tau_i`**: - `g_e0` and `g_i0` are average conductances, representing baseline synaptic input when presumably no activity occurs. - `std_e` and `std_i` denote the standard deviation, reflecting variability in synaptic conductance. - `tau_e` and `tau_i` represent the time constants of the respective conductances, relating to how quickly synapses integrate inputs over time. ## Implications for Neuronal Behavior 1. **Integration of Synaptic Inputs**: The effective membrane potential and neuronal excitability depend not only on instantaneous synaptic conductances (`g_e` and `g_i`) but also on their dynamic fluctuations over time. 2. **Output Current**: The resultant synaptic current `i` is the combination of the contributions from excitatory and inhibitory conductances applied across their respective driving forces. This fluctuating conductance model thus serves as a sophisticated tool to study the dynamic and complex nature of synaptic inputs that neurons constantly experience, facilitating a deeper understanding of neuronal behavior in the face of synaptic noise.