Information-Theoretic Approach and Fundamental Limits of Resolving Two Closely-Timed Neuronal Spikes in Mouse Brain Calcium Imaging

October 19, 2018

Information-Theoretic Approach and Fundamental Limits of Resolving Two Closely-Timed Neuronal Spikes in Mouse Brain Calcium Imaging

Calcium imaging has become a standard tool in neuroscience to record neural activity over large populations of neurons. Calcium sensor kinetics and signal-to-noise ratio significantly impact the precision of spike time estimation and spike detectability from the recorded optical signals. Due to the slow-dynamics of the calcium sensors, fluorescence transients generated by action potentials (APs) accumulate during periods of rapid activity. In such cases, the detection and separation of individual spikes is challenging due the unknown amplitude of single AP-induced transients and the nonlinear relationship between calcium dynamics and fluorescence response, especially in high firing rates. Although several groups have tackled the problem of firing rate inference or spike train extraction from the observed fluorescence signals, few of these studies have conducted theoretical performance limit analysis. Such theoretical analysis can aid in future spike detection approaches and in experimental design for optimal spike detectability. In this paper, we extend previous studies by conducting theoretical performance limits analysis in the case of two temporally overlapping fluorescence waveforms. Our work is based on the developed statistical and information theoretic tools for estimating the fundamental resolution of optical systems. Using these tools, we quantify resolution and the theoretical bound on the precision of estimating the inter-spike-interval (ISI) based on Poisson statistics and under different experimental setups. We use Monte-Carlo simulations with biologically derived parameters to numerically obtain the minimum detectable ISI and evaluate the performance of our estimators. Our results show that attaining resolution finer than the peak time of the calcium sensor is possible and the statistically optimal ISI estimators closely approach the theoretical lower bounds.

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