# Biological Basis of the Fluctuating Conductance Model Code The code is part of a computational model that aims to replicate the stochastic nature of synaptic inputs in neurons, specifically focusing on the fluctuation of synaptic conductances due to synaptic bombardment. The key biological aspects modeled in the code include: ## Synaptic Bombardment In vivo, neurons in the central nervous system are continuously bombarded by synaptic inputs, which are typically a mix of excitatory and inhibitory signals. This synaptic bombardment creates a background activity that can significantly influence neuronal behavior and responsiveness. ## Fluctuating Conductances The model employs two fluctuating conductances, \(g_e(t)\) for excitatory synapses and \(g_i(t)\) for inhibitory synapses. These conductances are key components of synaptic transmission, where: - **Excitatory Conductance \(g_e(t)\):** Represents the influx of positively charged ions through excitatory synapses, usually driven by the neurotransmitter glutamate. This influx typically depolarizes the neuron. - **Inhibitory Conductance \(g_i(t)\):** Represents the influx of negatively charged ions or the efflux of positively charged ions through inhibitory synapses, usually driven by neurotransmitters like GABA. This usually hyperpolarizes the neuron. ## Reversal Potentials The code defines reversal potentials (E_e and E_i) for excitatory and inhibitory conductances, which are typical for neurons: - **E_e (0 mV):** Approximates the reversal potential for glutamate-mediated excitatory postsynaptic potentials. - **E_i (-75 mV):** Approximates the reversal potential for GABA-mediated inhibitory postsynaptic potentials. ## Noise Representation The conductances are modeled as Ornstein-Uhlenbeck (OU) stochastic processes, introducing a random, yet temporally correlated, fluctuation: - **Noise in Conductances:** Random fluctuations in synaptic conductances are represented using Gaussian white noise. This reflects the variability seen in real synaptic input due to spontaneous neurotransmitter release and asynchronous input timing. - **Parameters of OU Process:** The time constants (\(\tau_e\) and \(\tau_i\)) and standard deviations (\(\text{std}_e\) and \(\text{std}_i\)) are set to reflect biologically plausible synaptic kinetics and variability. ## Biological Implications - **Temporal Correlations:** The time constants (\(\tau\)) imply that this model captures the temporal correlations of synaptic inputs. In reality, synaptic inputs are not entirely random but exhibit some temporal dependencies due to the nature of neurotransmitter release and subsequent receptor kinetics. - **Synaptic Variability:** By introducing variability in \(g_e(t)\) and \(g_i(t)\), this model simulates the natural variability and noise in synaptic transmission, providing a more realistic representation of neuronal input in contrast to static models. The code thus provides a framework for simulating synaptic input in a neuron's environment. This model offers insights into how fluctuating synaptic inputs can affect neuronal dynamics, potentially impacting information processing and signal integration in neural circuits.