Effective and efficient neural networks for spike inference from in vivo calcium imaging

Calcium imaging provides advantages in monitoring large populations of neuronal activities simultaneously. However, it lacks the signal quality provided by neural spike recording in traditional electrophysiology. To address this issue, we developed a supervised data-driven approach to extract spike information from calcium signals. We propose the ENS2 (effective and efficient neural networks for spike inference from calcium signals) system for spike-rate and spike-event predictions using ΔF/F0 calcium inputs based on a U-Net deep neural network. When testing on a large, ground-truth public database, it consistently outperformed state-of-the-art algorithms in both spike-rate and spike-event predictions with reduced computational load. We further demonstrated that ENS2 can be applied to analyses of orientation selectivity in primary visual cortex neurons. We conclude that it would be a versatile inference system that may benefit diverse neuroscience studies.

Calcium Imaging and the Curse of Negativity

The imaging of neuronal activity using calcium indicators has become a staple of modern neuroscience. However, without ground truths, there is a real risk of missing a significant portion of the real responses. Here, we show that a common assumption, the non-negativity of the neuronal responses as detected by calcium indicators, biases all levels of the frequently used analytical methods for these data. From the extraction of meaningful fluorescence changes to spike inference and the analysis of inferred spikes, each step risks missing real responses because of the assumption of non-negativity. We first show that negative deviations from baseline can exist in calcium imaging of neuronal activity. Then, we use simulated data to test three popular algorithms for image analysis, CaImAn, suite2p, and CellSort, finding that suite2p may be the best suited to large datasets. We also tested the spike inference algorithms included in CaImAn, suite2p, and Cellsort, as well as the dedicated inference algorithms MLspike and CASCADE, and found each to have limitations in dealing with inhibited neurons. Among these spike inference algorithms, FOOPSI, from CaImAn, performed the best on inhibited neurons, but even this algorithm inferred spurious spikes upon the return of the fluorescence signal to baseline. As such, new approaches will be needed before spikes can be sensitively and accurately inferred from calcium data in inhibited neurons. We further suggest avoiding data analysis approaches that, by assuming non-negativity, ignore inhibited responses. Instead, we suggest a first exploratory step, using k-means or PCA for example, to detect whether meaningful negative deviations are present. Taking these steps will ensure that inhibition, as well as excitation, is detected in calcium imaging datasets.

Improved spike inference accuracy by estimating the peak amplitude of unitary [Ca2+ ] transients in weakly GCaMP6f-expressing hippocampal pyramidal cells

KEY POINTS

The amplitude of unitary, single action potential-evoked [Ca²⁺ ] transients negatively correlates with GCaMP6f expression, but displays large variability among hippocampal pyramidal cells with similarly low expression levels. The summation of fluorescence signals is frequency-dependent, supralinear and also shows remarkable cell-to-cell variability. The main source of spike inference error is variability in the peak amplitude, and not in the decay or supralinearity. We developed two procedures to estimate the peak amplitudes of unitary [Ca²⁺ ] transients and show that spike inference performed with MLspike using these unitary amplitude estimates in weakly GCaMP6f-expressing cells results in error rates of ∼5%.

ABSTRACT

Investigating neuronal activity using genetically encoded Ca²⁺ indicators in behaving animals is hampered by inaccuracies in spike inference from fluorescent tracers. Here we combine two-photon [Ca²⁺ ] imaging with cell-attached recordings, followed by post hoc determination of the expression level of GCaMP6f, to explore how it affects the amplitude, kinetics and temporal summation of somatic [Ca²⁺ ] transients in mouse hippocampal pyramidal cells (PCs). The amplitude of unitary [Ca²⁺ ] transients (evoked by a single action potential) negatively correlates with GCaMP6f expression, but displays large variability even among PCs with similarly low expression levels. The summation of fluorescence signals is frequency-dependent, supralinear and also shows remarkable cell-to-cell variability. We performed experimental data-based simulations and found that spike inference error rates using MLspike depend strongly on unitary peak amplitudes and GCaMP6f expression levels. We provide simple methods for estimating the unitary [Ca²⁺ ] transients in individual weakly GCaMP6f-expressing PCs, with which we achieve spike inference error rates of ∼5%.

Robustness of Spike Deconvolution for Neuronal Calcium Imaging

Calcium imaging is a powerful method to record the activity of neural populations in many species, but inferring spike times from calcium signals is a challenging problem. We compared multiple approaches using multiple datasets with ground truth electrophysiology and found that simple non-negative deconvolution (NND) outperformed all other algorithms on out-of-sample test data. We introduce a novel benchmark applicable to recordings without electrophysiological ground truth, based on the correlation of responses to two stimulus repeats, and used this to show that unconstrained NND also outperformed the other algorithms when run on "zoomed out" datasets of ∼10,000 cell recordings from the visual cortex of mice of either sex. Finally, we show that NND-based methods match the performance of a supervised method based on convolutional neural networks while avoiding some of the biases of such methods, and at much faster running times. We therefore recommend that spikes be inferred from calcium traces using simple NND because of its simplicity, efficiency, and accuracy.SIGNIFICANCE STATEMENT The experimental method that currently allows for recordings of the largest numbers of cells simultaneously is two-photon calcium imaging. However, use of this powerful method requires that neuronal firing times be inferred correctly from the large resulting datasets. Previous studies have claimed that complex supervised learning algorithms outperform simple deconvolution methods at this task. Unfortunately, these studies suffered from several problems and biases. When we repeated the analysis, using the same data and correcting these problems, we found that simpler spike inference methods perform better. Even more importantly, we found that supervised learning methods can introduce artifactual structure into spike trains, which can in turn lead to erroneous scientific conclusions. Of the algorithms we evaluated, we found that an extremely simple method performed best in all circumstances tested, was much faster to run, and was insensitive to parameter choices, making incorrect scientific conclusions much less likely.