Quantifying bursting neuron activity from calcium signals using blind deconvolution

Abstract

Advances in calcium imaging have enabled studies of the dynamic activity of both individual neurons and neuronal assemblies. However, challenges, such as unknown nonlinearities in the spike–calcium relationship, noise, and the often relatively low temporal resolution of the calcium signal compared to the time-scale of spike generation, restrict the accurate estimation of action potentials from the calcium signal. Complex neuronal discharge, such as the activity demonstrated by bursting and rhythmically active neurons, represents an even greater challenge for reconstructing spike trains based on calcium signals. We propose a method using blind calcium signal deconvolution based on an information-theoretic approach. This model is meant to maximise the output entropy of a nonlinear filter where the nonlinearity is defined by the cumulative distribution function of the spike signal. We tested our maximum entropy (ME) algorithm using bursting olfactory receptor neurons (bORNs) of the lobster olfactory organ. The advantage of the ME algorithm is that the filter can be trained online based only on the statistics of the spike signal, without any assumptions regarding the unknown transfer function characterizing the relation between the spike and calcium signal. We show that the ME method is able to more accurately reconstruct the timing of the first and last spikes of a burst compared to other methods and that it improves the temporal precision fivefold compared to direct timing resolution of calcium signal.

Benchmarking Spike Rate Inference in Population Calcium Imaging

“…To solve this problem of spike inference, several different approaches have been proposed, including template-matching (Greenberg et al, 2008; Grewe et al, 2010; Oñativia et al, 2013), deconvolution (Park et al, 2013; Yaksi and Friedrich, 2006) and approximate Bayesian inference (Pnevmatikakis et al, 2016, 2013; Vogelstein et al, 2010, 2009). These methods have in common that they assume a forward generative model of calcium signal generation which is then inverted to infer spike times.…”

Error estimation for reconstruction of neuronal spike firing from fast calcium imaging

“…Despite the advances in reconstruction of neuronal spiking from Ca 2+ traces [5,9,15,19], only a few methods are available to estimate of the error range of the neuronal spiking reconstruction, mainly due to the lack of a rigorous mathematical model to quantitatively describe the relationship between calcium transients and bursting electrical activity. To overcome this problem, we employed statistical methods to generate an analog signal similar to the real neural signal, and then used the error range of reconstructed spiking from the analog signal to approximate that of the real signal.…”

“…Various reconstruction methods have been developed to date and significant progress has been achieved [5,[7][8][9][10][11][12][13][14]. However, there is no error estimation method that evaluates the corresponding reconstruction results associated with unclear nonlinearities in the spikecalcium relationship [9,15,16], contamination of signals from other cellular parts [4], system noise [17], and the often relatively low temporal resolution of the calcium signal recording compared to the electrical signal [14], along with the lack of a strict mathematical model describing the relationship between the Ca 2+ trace and spike firing (especially burst firing) [18,19].…”

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

“…), deconvolution (Yaksi & Friedrich, ; Park et al . ; Friedrich et al . ), approximate Bayesian inference (Vogelstein et al .…”

“…Despite these properties, APs cannot be directly inferred from the fluorescent transients with millisecond temporal resolution (Jercog et al 2016;Lin & Schnitzer, 2016). To overcome this limitation, several approaches have been developed to determine AP firing underlying the fluorescent traces: template-matching (Greenberg et al 2008;Grewe et al 2010;Onativia et al 2013), deconvolution (Yaksi & Friedrich, 2006;Park et al 2013;Friedrich et al 2017), approximate Bayesian inference (Vogelstein et al 2009;Pnevmatikakis et al 2016) and supervised learning techniques (Sasaki et al 2008;Theis et al 2016), but the accuracy of estimation for high-frequency events is still only 40-60% (Lin & Schnitzer, 2016;Theis et al 2016). Deneux et al (2016) improved spike estimation performance by introducing baseline drift (accounting for low-frequency, large-amplitude baseline fluctuations) and non-linearity of the indicator (p nonlin ).…”