  Quantification of neuronal correlations in neuron populations helps us to
understand neural coding rules. Such quantification could also reveal how
neurons encode information in normal and disease conditions like Alzheimer's
and Parkinson's. While neurons communicate with each other by transmitting
spikes, there would be a change in calcium concentration within the neurons
inherently. Accordingly, there would be correlations in calcium spike trains
and they could have heterogeneous memory structures. In this context,
estimation of mutual information rate in calcium spike trains assumes primary
significance. However, such estimation is difficult with available methods
which would consider longer blocks for convergence without noticing that
neuronal information changes in short time windows. Against this backdrop, we
propose a faster method that exploits the memory structures in pair of calcium
spike trains to quantify mutual information shared between them. Our method has
shown superior performance with example Markov processes as well as
experimental spike trains. Such mutual information rate analysis could be used
to identify signatures of neuronal behavior in large populations in normal and
abnormal conditions.
