Robust and consistent measures of pattern separation based on information theory and demonstrated in the dentate gyrus

Pattern separation is a valuable computational function performed by neuronal circuits, such as the dentate gyrus, where dissimilarity between inputs is increased, reducing noise and increasing the storage capacity of downstream networks. Pattern separation is studied from both in vivo experimental and computational perspectives and, a number of different measures (such as orthogonalisation, decorrelation, or spike train distance) have been applied to quantify the process of pattern separation. However, these are known to give conclusions that can differ qualitatively depending on the choice of measure and the parameters used to calculate it. We here demonstrate that arbitrarily increasing sparsity, a noticeable feature of dentate granule cell firing and one that is believed to be key to pattern separation, typically leads to improved classical measures for pattern separation even, inappropriately, up to the point where almost all information about the inputs is lost. Standard measures therefore both cannot differentiate between pattern separation and pattern destruction, and give results that may depend on arbitrary parameter choices. We propose that techniques from information theory, in particular mutual information, transfer entropy, and redundancy, should be applied to penalise the potential for lost information (often due to increased sparsity) that is neglected by existing measures. We compare five commonly-used measures of pattern separation with three novel techniques based on information theory, showing that the latter can be applied in a principled way and provide a robust and reliable measure for comparing the pattern separation performance of different neurons and networks. We demonstrate our new measures on detailed compartmental models of individual dentate granule cells and a dentate microcircuit, and show how structural changes associated with epilepsy affect pattern separation performance. We also demonstrate how our measures of pattern separation can predict pattern completion accuracy. Overall, our measures solve a widely acknowledged problem in assessing the pattern separation of neural circuits such as the dentate gyrus, as well as the cerebellum and mushroom body. Finally we provide a publicly available toolbox allowing for easy analysis of pattern separation in spike train ensembles.