Quantifying bursting neuron activity from calcium signals using blind deconvolution.

Advances in calcium imaging have enabled studies of the dynamic activity of both individual neurons and neuronal assemblies. However, challenges, such as unknown nonlinearities in the spike-calcium relationship, noise, and the often relatively low temporal resolution of the calcium signal compared to the time-scale of spike generation, restrict the accurate estimation of action potentials from the calcium signal. Complex neuronal discharge, such as the activity demonstrated by bursting and rhythmically active neurons, represents an even greater challenge for reconstructing spike trains based on calcium signals. We propose a method using blind calcium signal deconvolution based on an information-theoretic approach. This model is meant to maximise the output entropy of a nonlinear filter where the nonlinearity is defined by the cumulative distribution function of the spike signal. We tested our maximum entropy (ME) algorithm using bursting olfactory receptor neurons (bORNs) of the lobster olfactory organ. The advantage of the ME algorithm is that the filter can be trained online based only on the statistics of the spike signal, without any assumptions regarding the unknown transfer function characterizing the relation between the spike and calcium signal. We show that the ME method is able to more accurately reconstruct the timing of the first and last spikes of a burst compared to other methods and that it improves the temporal precision fivefold compared to direct timing resolution of calcium signal.