Abstract
A major goal in neuroscience is to estimate neural connectivity from large scale extracellular recordings of neural activity in vivo. This is challenging in part because any such activity is modulated by the unmeasured external synaptic input to the network, known as the common input problem. Many different measures of functional connectivity have been proposed in the literature, but their direct relationship to synaptic connectivity is often assumed or ignored. For in vivo data, measurements of this relationship would require a knowledge of ground truth connectivity, which is nearly always unavailable. Instead, many studies use in silico simulations as benchmarks for investigation, but such approaches necessarily rely upon a variety of simplifying assumptions about the simulated network and can depend on numerous simulation parameters. We combine neuronal network simulations, mathematical analysis, and calcium imaging data to address the question of when and how functional connectivity, synaptic connectivity, and latent external input variability can be untangled. We show numerically and analytically that, even though the precision matrix of recorded spiking activity does not uniquely determine synaptic connectivity, it is in practice often closely related to synaptic connectivity. This relation becomes more pronounced when the spatial structure of neuronal variability is jointly considered.
Highlights
Modern interest in connectivity inference in neuroscience is quite broad in scope, ranging in scale from the microscopic properties of dendritic arbors to macroscopic cooperation across whole brain regions (Magrans de Abril et al, 2018)
The accuracy of inference for generalized linear point-process model (GLM) has been evaluated in silico using simulations of non-linear Hawkes process models (Pernice et al, 2011)
Functional connectivity inferred by GLMs applied to Hawkes process models is often interpreted not to approximate actual synaptic connectivity, but rather to represent the “effective” interaction between neurons with respect to the model network (Feldt et al, 2011; Poli et al, 2016)
Summary
Modern interest in connectivity inference in neuroscience is quite broad in scope, ranging in scale from the microscopic properties of dendritic arbors to macroscopic cooperation across whole brain regions (Magrans de Abril et al, 2018). Previous work has evaluated the relationship between functional and synaptic connectivity when GLMs are fit to spiking data subsampled from simulations of networks of leaky IF neurons (Lutcke et al, 2013; Zaytsev et al, 2015). They assessed recovery of the ground truth structure from the in silico biophysical model against inferred coupling in the statistical model, but found relatively low accuracy of recovery overall. We present a mean-field method for inferring properties of external latent variability for a neural circuit in mouse visual cortex
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