The provided code snippet is a computational model designed to simulate neural networks composed of spiking neurons, specifically focusing on the simulation of excitatory and inhibitory interactions within the network. This model adheres to the benchmarks of a study by Brette et al. (2007), which reviews tools and strategies for simulating networks of spiking neurons, and it implements a model from Vogels & Abbott (2005). Below is a summary of the biological basis: ### Biological Basis #### Neuron Types The code models a network comprising **excitatory** and **inhibitory neurons**: - **Excitatory Neurons**: These neurons increase the likelihood of the neurons they connect to firing action potentials. In the code, excitatory cells outnumber inhibitory cells by a ratio `r_ei = 4.0`. - **Inhibitory Neurons**: In contrast, these neurons decrease the likelihood of action potentials. The proportion and functionality of these neurons determine the balance of excitation and inhibition in the network. #### Synaptic Interactions The model uses two benchmarks to simulate synaptic interactions: - **CUBA (Current-Based)**: In this configuration, synapses convey currents proportional to the conductance and the difference between the reversal potential of the synapse and the membrane potential. - Requires a different leak reversal potential (`E_leak = -49 mV`). - **COBA (Conductance-Based)**: Here, synapses influence the neuron's membrane potential by altering the conductance, making the synaptic input a dynamic variable. - Operates with a leak potential of `E_leak = -60 mV`. #### Membrane Dynamics The modeled neurons are **integrate-and-fire (IF)** neurons, characterized by: - **Passive Membrane Properties**: Defined by parameters like membrane resistance (`Rm`), membrane capacitance (`cm`), and leak conductance (`g_leak`). These properties determine how the neuron integrates incoming synaptic inputs. - **Threshold and Reset Dynamics**: Neurons have a threshold potential (`v_thresh = -50 mV`) for generating spikes and reset to a lower potential (`v_reset = -60 mV`) after spiking, mimicking action potential firing and refractory periods. #### Stochastic Processes The model introduces variability and randomness through: - **Random Input (Poisson Spike Train)**: Some neurons receive external input as a Poisson process, which provides a stochastic component similar to real neuronal networks. - **Random Initial Membrane Potentials**: Neurons start with potentials randomly distributed between reset potential and threshold, introducing diversity in firing patterns. #### Neuronal Parameters The model incorporates biologically realistic parameters: - **Time Constants**: Membrane time constant (`tau_m = 20 ms`), synaptic time constants for excitatory (`tau_exc = 5 ms`) and inhibitory synapses (`tau_inh = 10 ms`) reflect the temporal dynamics of neuronal membranes and synaptic integration. - **Reversal Potentials**: Defined for excitatory (`Erev_exc = 0 mV`) and inhibitory (`Erev_inh = -80 mV`) synapses, representing typical ion channel dynamics. ### Conclusion Overall, this code provides a means to simulate the dynamics of spiking neural networks using biophysically inspired parameters and mechanisms, emphasizing the role of excitation and inhibition balance and the role of synaptic interactions in neural computation. It allows researchers to explore how the interplay of these components leads to complex emergent behaviors within neural systems.