Abstract
OBJECTIVE: Inferring the times of sequences of action potentials (APs) (spike trains) from neurophysiological data is a key problem in computational neuroscience. The detection of APs from two-photon imaging of calcium signals offers certain advantages over traditional electrophysiological approaches, as up to thousands of spatially and immunohistochemically defined neurons can be recorded simultaneously. However, due to noise, dye buffering and the limited sampling rates in common microscopy configurations, accurate detection of APs from calcium time series has proved to be a difficult problem. APPROACH: Here we introduce a novel approach to the problem making use of finite rate of innovation (FRI) theory (Vetterli et al 2002 IEEE Trans. SIGNAL PROCESS: 50 1417-28). For calcium transients well fit by a single exponential, the problem is reduced to reconstructing a stream of decaying exponentials. Signals made of a combination of exponentially decaying functions with different onset times are a subclass of FRI signals, for which much theory has recently been developed by the signal processing community. Main results. We demonstrate for the first time the use of FRI theory to retrieve the timing of APs from calcium transient time series. The final algorithm is fast, non-iterative and parallelizable. Spike inference can be performed in real-time for a population of neurons and does not require any training phase or learning to initialize parameters. SIGNIFICANCE: The algorithm has been tested with both real data (obtained by simultaneous electrophysiology and multiphoton imaging of calcium signals in cerebellar Purkinje cell dendrites), and surrogate data, and outperforms several recently proposed methods for spike train inference from calcium imaging data.
🔬 Techniques
💻 Software
✨ Fluorophores
🧪 Sample Preparation
🏭 Microscope Brands
🔴 Lasers
💻 Software Details
🏛️ Research Organizations (ROR)
Affiliated research institutions:
📋 Methods
2.1.
Experimental methods
The data used in this study, and the experimental methods used to collect them, have been previously described ( Schultz et al 2009 ). Briefly, Sprague-Dawley rats (P18–P29) were anaesthetized with urethane (1.2 g kg −1 ) or with ketamine (50 mg kg −1 ) / xylazine (5 mg kg −1 ). A craniotomy was made over area Crus IIa of the cerebellum, filled with 1.5–2% agarose in Ringer’s solution, and a coverslip clamped above the agarose to suppress brain movement, while leaving a window open for microelectrode access. A micropipette was inserted to a depth of around 100–200 μ m below the pia mater, and AM-ester calcium dye (Oregon Green BAPTA-1 AM) pressure-ejected. Imaging was performed from 30 min following dye ejection, using a two-photon laser scanning microscope (Prairie Technologies). A pulsed Titanium:Sapphire laser was used for excitation, operating at 810 nm (MaiTai, SpectraPhysics) with
📊 Figures
Figure A1
Filtering process of a stream of decaying exponentials.
Figure 1
Simultaneous multiphoton calcium imaging with electrophysiology. (a) Maximum intensity projection showing juxtacellular recording from a Purkinje cell dendrite. The tissue was loaded with Oregon Green...
Figure 2
Filtering and sampling.
Figure 3
First order E-spline that reproduces two different exponential functions. ( a ) First order E-spline. ( b ) Reproduction of e u22122 . ( c ) Reproduction of e + t /2 .
Figure 4
The annihilating filter is a cascaded interconnection of unitary filters with zeros at u k . Any signal formed by a linear combination of the exponential sequences u k n is filtered out.
Figure 5
Filtering process of the measured signal.
Figure 6
Fluorescence signal processing with a sliding window. For each time interval, the number of spikes within that interval is first estimated and then the location of each spike is retrieved.
Figure 7
Double consistency spike search with real data. (a) and (b) show the detected locations in red and the locations of the original spikes in blue for two different window sizes. In (a) the algorithm est...
Figure 8
Surrogate data. Temporal resolution T res = 147.2 ms and SNR = 10 dB.
Figure 9
Algorithmu2019s performance measurement with surrogate data. The surrogate data contains 1000 spikes in a time interval of 2000 s. For each noise level, the experiment has been repeated for 100 differ...
Figure 10
Simulations showing FRI algorithm achieving better performances in spike train inference than the fast deconvolution technique from Vogelstein et al (2010) and different filtering and thresholding app...
Figure images are served from the NIH/NLM PubMed Central Open Access Subset or Europe PMC; copyright remains with the publishers and authors.
💬 Discussion
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