Spike inference from calcium imaging using sequential Monte Carlo methods

Joshua Vogelstein, Brendon Watson, Adam Packer, Bruno Jedynak, Rafael Yuste, and Liam Paninski

Biophysical Journal 97: 636-655

As recent advances in calcium sensing technologies enable us to simultaneously image many neurons, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. While the observations here are fluorescence images, the signals of interest - spike trains and/or time varying intracellular calcium concentrations - are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing a family of particle filters based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing errorbars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation-maximization with only a very limited amount of data, without the requirement of any simultaneous electrophysiology and imaging experiments.
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