A zero-inflated gamma model for post-deconvolved calcium imaging traces

Abstract

Calcium imaging is a critical tool for measuring the activity of large neural populations.Much effort has been devoted to developing "pre-processing" tools applied to calcium video data, addressing the important issues of e.g., motion correction, denoising, compression, demixing, and deconvolution. However, computational modeling of deconvolved calcium signals (i.e., the estimated activity extracted by a pre-processing pipeline) is just as critical for interpreting calcium measurements. Surprisingly, these issues have to date received significantly less attention. To fill this gap, we examine the statistical properties of the deconvolved activity estimates, and propose several density models for these random signals. These models include a zero-inflated gamma (ZIG) model, which characterizes the calcium responses as a mixture of a gamma distribution and a point mass which serves to model zero responses. We apply the resulting models to neural encoding and decoding problems. We find that the ZIG model outperforms simpler models (e.g., Poisson or Bernoulli models) in the context of both simulated and real neural data, and can therefore play a useful role in bridging calcium imaging analysis methods with tools for analyzing activity in large neural populations.

Model-based decoupling of evoked and spontaneous neural activity in calcium imaging data

“…If instead factor activity states were constrained to vary smoothly and have high autocorrelation (e.g., under a Gaussian process prior), the predicted fluorescence transients would be PLOS COMPUTATIONAL BIOLOGY inaccurately prolonged following the GCaMP convolution. Indeed, calcium influx is typically well-described by sparse spike-and-slab models [46], and an exponential prior that specifically omits factor autocorrelation allows us to compromise between sparsity, model simplicity, and computational tractability.…”

Parallel inference of hierarchical latent dynamics in two-photon calcium imaging of neuronal populations

“…While we have demonstrated how powerful VaLPACa can be as a tool for analysing calcium imaging data, it is likely not the only way to approach this problem. Alternative continious approximations to spike counts could still be explored, such as the zero-inflated Gamma model 36 or techniques using the Gumbel-Softmax trick 20,37 . An interesting approach that we did not explore is to generate fluorescence traces directly from firing rates by marginalising over spike counts 38 , in which case a ladder architecture might not be necessary.…”

Neural encoding models for multivariate optical imaging data

“…(Indeed, if ξ = 1, α = 1, and J = 0, this reduces to the CILVA model). The ZIW is closely related to the zero-inflated gamma, which was recently shown by Wei et al [169] to be the preferred model for deconvolved calcium traces due to their ability to flexibly account for the frequent case of having exactly zero calcium influx in a given imaging bin (which is therefore important for accurately sampling from the posterior distribution), while also having an adjustable shape and scale for positive neural activity. For our purposes the ZIW offers similar flexibility, but the Weibull has a tractable inverse cumulative distribution function (inverse CDF), allowing samples to be drawn by passing a uniformly distributed random variable through a differentiable transformation.…”

“…However, while solving such optimisation problems is central to obtaining usable scientific data from raw calcium imaging recordings, few models have addressed the subsequent stage of analysis, which focuses on relating the segmented, denoised calcium signals to experimentally relevant variables using principled statistical methods. Several recent examples include statistical modelling of calcium responses evoked by sensory stimuli [169], internal factors [170], and photostimulation [128]. In ref.…”

“…While this model is effective for decoupling stimulus-driven calcium responses from ongoing spontaneous activity, it can be improved in several respects. First, recent work [169] has noted that, because a substantial fraction of calcium influx is exactly zero, spike-and-slab distributions such as the zero-inflated gamma are better suited to modelling calcium influx compared to the exponential prior used in ref. [170].…”