The provided code models fluctuating synaptic conductances in a neuronal cell, representing synaptic input from a network of neurons. It captures the biological phenomenon of synaptic bombardment, where a neuron receives continuous, fluctuating synaptic inputs due to the activity of surrounding neurons.

Biological Basis

1. Excitatory and Inhibitory Conductances:

   • Excitatory Conductances (g_e): Represent synaptic inputs that depolarize the neuron. This is modeled with a reversal potential E_e of 0 mV, typical for excitatory synapses mediated by neurotransmitters like glutamate.
   • Inhibitory Conductances (g_i): Represent synaptic inputs that hyperpolarize the neuron, inhibiting its activity. The reversal potential E_i is set at -75 mV, simulating inhibition typically mediated by neurotransmitters like GABA.

2. Synaptic Variability:

   • Synaptic conductances are not constant but fluctuate over time, modeled here as Gaussian random processes. This fluctuation is biologically realistic, reflecting the dynamic and stochastic nature of synaptic transmission resulting from varying neurotransmitter release and postsynaptic receptor dynamics.
   • The code uses parameters for the standard deviations of excitatory (std_e) and inhibitory (std_i) conductances, reflecting biological variability in synaptic strength.

3. Time Constants (tau_e and tau_i):

   • The time constants for excitatory (tau_e) and inhibitory (tau_i) conductances reflect the kinetics of synaptic currents, with excitatory synaptic inputs typically having shorter durations than inhibitory ones. These constants determine how quickly the conductances can change over time, affecting the integration of synaptic inputs.

4. Stochastic Modeling:

   • The model utilizes random number generation to simulate the stochastic processes underlying conductance changes. It accounts for the probabilistic nature of neurotransmitter release and the activation of postsynaptic receptors.

5. Homeostatic Conductance Baselines (g_e0 and g_i0):

   • Baseline or average conductance values are provided (g_e0 and g_i0), which represent the mean synaptic input level the neuron experiences in a resting or homeostatic state.

6. Diffusion Coefficients (D_e and D_i):

   • These coefficients relate to the variance of the synaptic conductances over time, quantifying the extent of their fluctuation due to synaptic noise inherent in biological synapses.

Summary

The model captures the essence of fluctuating synaptic inputs that a neuron in a network might experience, with both excitatory and inhibitory components modulated by physiological parameters such as time constants, baseline conductance levels, and stochastic variability. This representation is critical for understanding how neurons integrate synaptic inputs and how this integration influences neuronal excitability and network activity.