NC-Network-of-LIF-Neurons-Coupled-by-Chemical-Synapses

This program generates a network of LIF neurons which are connected through chemical synapses. It solves LIF equation as follows:

where τ is the time constant of neuron, v is the membrane potential of the postsynaptic neuron, v_rest is the resting state membrane potential, I_ext is the external input, which is equivalent to a sensory stimulus or any input sourced from the activity of population of neurons nearby, and I_syn is accumulative synaptic inputs arrived from all the pre-synaptic neurons to the given post-synaptic one, which is calculated through

here, i is associated index of pre synaptic neurons, v is the postsynaptic potential, and E_syn is the synaptic reversal potential. Whether a synapse is excitatory or inhibitory is determined by E_syn. For inhibitory synapses, E_syn equals to E_syn_inh (here it is -80), and for excitatory ones the value is set to zero. g is maximal conductance of the synapse, and S represents the fraction of bound receptors. Its kinetics are described by the following equation,

where N is equivalent to the concentration of transmitters released into the synaptic cleft following the arrival of an action potential at the pre-synaptic terminal. Since the concentration of neurotransmitters in the cleft rises and falls very rapidly, it is assumed that N occurs as a rectangular pulse. α and β are the rate constants for transmitter binding to and unbinding from post-synaptic receptor, respectively. α and β and duration of N characterize the dynamics of post-synaptic potential (EPSP & IPSP). They directly specify the shape of S. (Destexhe, 1993)

This program returns 4 graphs. Figure(1) depicts the sub-threshold dynamics of neurons' membrane potential. Figure(2) represents the dynamics of N. It also shows the dynamics of S₁₂ and S₂₁, which is meant to demonstrate the typical profile of S signal, which in turn determine the input I_syn. You can produce EPSP and IPSP corresponding to NMDA, GABA_A, GABA_B, etc. by setting relevant values for α and β and therefore for the shape the S profile. Figure(3) demonstrates the accumulative synaptic inputs from pre-synaptic neurons arrived to the post-synaptic ones. Note that negative I_syn corresponds to EPSP and positive I_syn corresponds to IPSP (Consider the negative sign before I_syn in the LIF equation). Figure(4) is raster plot of the neuronal activity in the network.