Spike Inference from Calcium Imaging Using Sequential Monte Carlo Methods

Abstract

As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies, the signals of interest--spike trains and/or time varying intracellular calcium concentrations--are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing sequential Monte Carlo methods (particle filters) based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing error bars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence (e.g., refractoriness) of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate temporal superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation maximization with only a very limited amount of data (e.g., approximately 5-10 s or 5-40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.

Imaging Action Potentials with Calcium Indicators

“…Although significant advances have been made in this regard (see Vogelstein et al 2009Vogelstein et al , 2010, continued improvement appears necessary. …”

“…This is a difficult statistical problem for a number of reasons, including www.cshprotocols.org the low temporal resolution of the imaging (often <30 Hz) and, in some cases, the limited signal-to-noise ratio of the fluorescence observations (e.g., caused by indicator saturation). A number of groups have devised algorithms for extracting spiking activity from fluorescence observations, including thresholding (Mao et al 2001), template matching (Kerr et al 2005), linear deconvolution (Yaksi and Friedrich 2006;Holekamp et al 2008), support vector methods (Sasaki et al 2008), nonlinear Bayesian deconvolution via sequential Monte Carlo (particle filtering) (Vogelstein et al 2009), and fast non-negatively constrained optimization methods (Vogelstein et al 2010). Most of these approaches either explicitly or implicitly assume a model relating the spike trains to the fluorescence observations: The spike train is convolved with some linear filter (usually a simple exponential filter, although this may be generalized) to obtain the intracellular calcium concentration, and the fluorescence signal is essentially a noisy, possibly saturated version of the calcium.…”

“…Most of these approaches either explicitly or implicitly assume a model relating the spike trains to the fluorescence observations: The spike train is convolved with some linear filter (usually a simple exponential filter, although this may be generalized) to obtain the intracellular calcium concentration, and the fluorescence signal is essentially a noisy, possibly saturated version of the calcium. The parameters of this model may be estimated via standard statistical time-series methods if simultaneous observations of electrophysiological and imaging data are available or via the expectation-maximization algorithm if only imaging data are available (Vogelstein et al 2009). These latter approaches have been shown to perform well in a variety of experimental preparations, including both in vitro and in vivo data sets (see Fig.…”

Optimization of Stimulation Parameters for Targeted Activation of Multiple Neurons Using Closed-Loop Search Methods

“…Calcium signaling is dynamic and continuous within both neurons and glia associated with a neuronal population; therefore, there exists a low-level fluorescence that can be measured within these cell bodies due to the action of the calcium indicator as a chelator trapped with all cells. However, numerous studies have been published demonstrating the use of calcium indicators to infer neuronal spiking enabled by both the relatively fast and large change in measurable fluorescence at a neuronal cell body immediately following an action potential [35][36][37][38].…”

“…Processes 2017, 5, 81 5 of 21 calcium indicators to infer neuronal spiking enabled by both the relatively fast and large change in measurable fluorescence at a neuronal cell body immediately following an action potential [35][36][37][38]. The relative change in fluorescence, ΔF/F, was calculated by subtracting the baseline (an average of four pre-stimulus frames, 30 fps) from an average of four post-stimulus frames (30 fps) and dividing the difference by the baseline.…”