This program generates two LIF neurons which are coupled by a chemical synapse. It solves LIF equation as follows:
where v is the membrane potential of the postsynaptic neuron, I_ext is the external input, which can be a sensory stimulus or any input from the population activity of other neurons, vrest is the membrane potential of resting state, and τ is the time constant of neuron. Isyn is accumulative synaptic inputs arrived from all the pre-synaptic neurons to the given post-synaptic one, which is calculated through
where i is associated index of pre synaptic neurons, v is the postsynaptic potential, and Esyn is the synaptic reversal potential. Whether a synapse is excitatory or inhibitory is specified by E_syn. For inhibitory synapses, E_syn equals to E_syn_inh, 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.
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 and unbinding to post-synaptic receptor. 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) is raster plot of the two neurons. Figure(3) represents the dynamics of N and S, which determine the input Isyn. You can produce EPSP and IPSP corresponding to NMDA, GABAA, GABAB, etc. by setting relevant values for α and β and therefore for the shape the S profile. Figure(4) demonstrates the accumulative synaptic inputs from pre-synaptic neurons to the post-synaptic one. Note that negative Isyn corresponds to EPSP and positive Isyn corresponds to IPSP (Consider the negative sign before Isyn in the LIF equation).