Information theoretic analysis of action potential trains. II. Analysis of correlation among n neurons to deduce connection structure.

We propose a cross-correlational method based on information theory, which produces a network connection structure to account for observed patterns of action potential activity in multi-unit recordings. Firing probabilities and conditional probabilities are estimated from the action potential trains of n neurons. Two-point mutual information (2pMI) and joint conditional mutual information (JCMI) are calculated by using the estimated probabilities, and then the n-point mutual information (npMI) is calculated. A significant peak of npMI indicates that each neuron is connected to all other neurons at specified time differences, either directly or indirectly. To distinguish between direct and indirect connection, the two-point m-joint conditional mutual information (2pJCMI) is calculated over the peak region for each pair of neurons. A minimum effective connection structure among the n neurons can be deduced in this manner. The procedure for deducing the connection structure for three- and n-neuron networks is described. We apply this method to action potential trains produced by simulated neural networks. Some limitations of the method are also discussed.