Effects of collateral inhibition in a model of the immature rat cerebellar cortex: multineuron correlations

A model of the immature rat cerebellar cortex is used to simulate the effect of the inhibitory recurrent collateral axons of the Purkinje cells on the spike trains in the network. Inhibition induces an important overall change in the statistical characteristics of individual spike trains. It is also instrumental in producing a strong cooperativity between the different neurons. Moreover, a functional spatial anisotropy appears. A specific entropy index is used to analyze levels of information transfer between clustered and faraway neurons in the network. The formatting effect of recurrent collateral inhibition on spike trains and on network functional dynamics is studied by means of a model of the newborn rat cerebellar cortex. This immature structure has simpler morphological characteristics and fewer physiological parameters than the adult one. It is thus a good candidate for the comparison between experimental and theoretical data. The model network is made of 256 formal neurons (FN), arranged in a square lattice. Each neuron is coupled to its eight nearest neighbors by inhibitory links. All the parameters of the different elements of the model--in particular integration of inhibitory and excitatory inputs--are given anatomical and physiological values derived from biological data. Activities of single FNs and correlations between spatially distant ones are analyzed with classical statistical techniques as well as with a specific informational entropy method we introduce. Simulation results indicate that inhibition is instrumental in: (1) the transformation of the spike train characteristics. This includes a lengthening of the mean interspike interval as well as an overall change in the statistical distribution of intervals, with an emergence of long-lasting ones; (2) the functional structuration of the network. Inhibitory connections between nearest neighbors induce a strong cooperativity between FNs. Furthermore a clear spatial anisotropy occurs in the functioning of the network, with inhibitory effects extending beyond local connectivity in preferential directions. We propose an interpretation of this functional structuration in terms of the various routes followed by the inhibition, including relay effects. The parameters of the model (levels of activities, inhibition rules and connectivities) were varied in order to test the robustness of the above results. Finally, the results are compared with those obtained in an experimental situation.