Non-linear and Threshold Effects of Synaptic Connectivity on the Correlation Parameter of a System of Two Coupled

The influence and effect of connection strength between neurons is difficult to predict in complex networks and a complete and exhaustive analytical theory does not exist because of the extremely non-linearity of neural models, so numerical simulation of complex network are the sole reliable method. Here we devised a minimalistic approach, in which two linked neurons are studied and the role of connection strength between them is made apparent. We found that if the post-synaptic neuron has no external stimuli, correlation remains low until a discontinuity threshold that occurs about w = 0.15 or w = 0.4 depending on the neurons type tested. After the threshold, correlation grows in a quasi-linear trend ending on a plateau, depending again on the neurons type. Testing bursting and non-bursting neurons, we demonstrated that bursts favour better and quicker correlation between the two cells. In fact in all our tests, a pre-synaptic bursting neuron promote faster correlation against the other type of non-bursting neurons (regular and fast spiking). The presence of a discontinuous dependence of connection strength is a previously known phenomenon, but has been studied here for the first time in controlled and systematic conditions for isolated neuron pairs and for different classes of neurons. When the bursting is stimulating cells in presence of a constant external input, a differentiation between neurons with strong frequency adaptation and other types of cells emerges