Functional connectivity estimation over large networks at cellular resolution based on electrophysiological recordings and structural prior (original) (raw)
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A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data
The Annals of Applied …, 2011
Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation-Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L1 penalization methods.
Statistical Learning of Neuronal Functional Connectivity
Technometrics, 2016
Identifying the network structure of a neuron ensemble beyond the standard measure of pairwise correlations is critical for understanding how information is transferred within such a neural population. However, the spike train data pose significant challenges to conventional statistical methods due to not only the complexity, massive size, and large scale, but also high dimensionality. In this article, we propose a novel "structural information enhanced" (SIE) regularization method for estimating the conditional intensities under the generalized linear model (GLM) framework to better capture the functional connectivity among neurons. We study the consistency of parameter estimation of the proposed method. A new "accelerated full gradient update" algorithm is developed to efficiently handle the complex penalty in the SIE-GLM for large sparse datasets applicable to spike train data. Simulation results indicate that our proposed method outperforms existing approaches. An application of the proposed method to a real spike train dataset, obtained from the prelimbic region of the prefrontal cortex of adult male rats when performing a T-maze based delayed-alternation task of working memory, provides some insight into the neuronal network in that region.
Bayesian inference of functional connectivity and network structure from spikes
Neural Systems and …, 2009
Current multi-electrode techniques enable the simultaneous recording of spikes from hundreds of neurons. To study neural plasticity and network structure it is desirable to infer the underlying functional connectivity between the recorded neurons. Functional connectivity is defined by a large number of parameters, which characterize how each neuron influences the other neurons. A Bayesian approach that combines information from the recorded spikes (likelihood) with prior beliefs about functional connectivity (prior) can improve inference of these parameters and reduce overfitting. Recent studies have used likelihood functions based on the statistics of point-processes and a prior that captures the sparseness of neural connections. Here we include a prior that captures the empirical finding that interactions tend to vary smoothly in time. We show that this method can successfully infer connectivity patterns in simulated data and apply the algorithm to spike data recorded from primary motor (M1) and premotor (PMd) cortices of a monkey. Finally, we present a new approach to studying structure in inferred connections based on a Bayesian clustering algorithm. Groups of neurons in M1 and PMd show common patterns of input and output that may correspond to functional assemblies.
Functional structure of cortical neuronal networks grown in vitro
Physical Review E, 2007
We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher point multi-informations between any two spike trains conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light into the functional connectivity arrangements of any three cells. We analyze the resultant connectivity graphs in light of other complex networks and demonstrate that, despite their ex vivo development, the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient, network diameter and assortative mixing. Specifically we show that these networks are weakly disassortative small world graphs, which differ significantly in their structure from randomized graphs with the same degree. We expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks, derived from time series data.
The functional structure of cortical neuronal networks grown in vitro
2007
We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher point multi-informations between any two spike trains conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light into the functional connectivity arrangements of any three cells. We analyze the resultant connectivity graphs in light of other complex networks and demonstrate that, despite their ex vivo development, the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontri...
Studying connectivity of neuronal cultures can provide insights for understanding brain networks but it is challenging to reveal neuronal connectivity from measurements. We apply a novel method that uses a theoretical relation between the time-lagged cross-covariance and the equal-time cross-covariance to reveal directed effective connectivity and synaptic weights of cortical neuron cultures at different days in vitro from multielectrode array recordings. Using a stochastic leaky-integrate-and-fire model, we show that the simulated spiking activity of the reconstructed networks can well capture the measured network bursts. The neuronal networks are found to be highly nonrandom with an over-representation of bidirectionally connections as compared to a random network of the same connection probability, with the fraction of inhibitory nodes comparable to the measured fractions of inhibitory neurons in various cortical regions in monkey, and have small-world topology with basic network...
A Morpho-Density Approach to Estimating Neural Connectivity
PLoS ONE, 2014
Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.
Medical Image Analysis, 2015
The ultimate goal of neuroscience is understanding the brain at a functional level. This requires the investigation of the structural connectivity at multiple scales: from the single-neuron micro-connectomics to the brain-region macro-connectomics. In this work, we address the study of connectomics at the intermediate mesoscale, introducing a probabilistic approach capable of reconstructing complex topologies of large neuronal networks. Suitable directional features are designed to model the local neuritic architecture and a feature-based particle filtering framework is proposed which allows the spatial tracking of neurites on microscopy images. The experimental results on cultures of increasing complexity, grown on High-Density Micro Electrode Arrays, show good stability and performance as compared to ground truth annotations drawn by domain experts. We also show how the method can be used to dissect the structural connectivity of inhibitory and excitatory subnetworks opening new perspectives towards the investigation of functional interactions among multiple cellular populations.
Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits
PLoS Biology, 2005
How different is local cortical circuitry from a random network? To answer this question, we probed synaptic connections with several hundred simultaneous quadruple whole-cell recordings from layer 5 pyramidal neurons in the rat visual cortex. Analysis of this dataset revealed several nonrandom features in synaptic connectivity. We confirmed previous reports that bidirectional connections are more common than expected in a random network. We found that several highly clustered three-neuron connectivity patterns are overrepresented, suggesting that connections tend to cluster together. We also analyzed synaptic connection strength as defined by the peak excitatory postsynaptic potential amplitude. We found that the distribution of synaptic connection strength differs significantly from the Poisson distribution and can be fitted by a lognormal distribution. Such a distribution has a heavier tail and implies that synaptic weight is concentrated among few synaptic connections. In addition, the strengths of synaptic connections sharing pre-or postsynaptic neurons are correlated, implying that strong connections are even more clustered than the weak ones. Therefore, the local cortical network structure can be viewed as a skeleton of stronger connections in a sea of weaker ones. Such a skeleton is likely to play an important role in network dynamics and should be investigated further.