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

Objective: Although optical imaging of neurons using fluorescent genetically encoded calcium sensors has enabled large-scale
in vivo
experiments, the sensors’ slow dynamics often blur closely timed action potentials into indistinguishable transients. While several previous approaches have been proposed to estimate the timing of individual spikes, they have overlooked the important and practical problem of estimating interspike interval (ISI) for overlapping transients.
Methods:
We use statistical detection theory to find the minimum detectable ISI under different levels of signal-to-noise ratio (SNR), model complexity, and recording speed. We also derive the Cramer–Rao lower bounds (CRBs) for the problem of ISI estimation. We use Monte-Carlo simulations with biologically derived parameters to numerically obtain the minimum detectable ISI and evaluate the performance of our estimators. Furthermore, we apply our detector to distinguish overlapping transients from experimentally obtained calcium imaging data.
Results:
Experiments based on simulated and real data across different SNR levels and recording speeds show that our algorithms can accurately distinguish two fluorescence signals with ISI on the order of tens of milliseconds, shorter than the waveform's rise time. Our study shows that the statistically optimal ISI estimators closely approached the CRBs.
Conclusion:
Our work suggests that full analysis using recording speed, sensor kinetics, SNR, and the sensor's stochastically distributed response to action potentials can accurately resolve ISIs much smaller than the fluorescence waveform's rise time in modern calcium imaging experiments.
Significance:
Such analysis aids not only in future spike detection methods, but also in future experimental design when choosing sensors of neuronal activity.