582 research outputs found
Statistical Inference for Assessing Functional Connectivity of Neuronal Ensembles With Sparse Spiking Data
The ability to accurately infer functional connectivity between ensemble neurons using experimentally acquired spike train data is currently an important research objective in computational neuroscience. Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons. However, unfavorable experimental conditions occasionally results in insufficient data collection due to factors such as low neuronal firing rates or brief recording periods, and in these cases, the standard maximum likelihood estimate becomes unreliable. The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data. Four inference methods were compared: maximum likelihood estimation, penalized maximum likelihood estimation, using either l2 or l1 regularization, and hierarchical Bayesian estimation based on a variational Bayes algorithm. Algorithmic performances were compared using well-established goodness-of-fit measures in benchmark simulation studies, and the hierarchical Bayesian approach performed favorably when compared with the other algorithms, and this approach was then successfully applied to real spiking data recorded from the cat motor cortex. The identification of spiking dependencies in physiologically acquired data was encouraging, since their sparse nature would have previously precluded them from successful analysis using traditional methods.National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant Grant R01-DA015644)National Institutes of Health (U.S.) (Grant Grant R01-HL08450
A Granger Causality Measure for Point Process Models of Ensemble Neural Spiking Activity
The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding
of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing
these interactions has not been established. Granger causality has proven to be an effective method for the analysis of the
directional interactions between multiple sets of continuous-valued data, but cannot be applied to neural spike train
recordings due to their discrete nature. This paper proposes a point process framework that enables Granger causality to be
applied to point process data such as neural spike trains. The proposed framework uses the point process likelihood
function to relate a neuron’s spiking probability to possible covariates, such as its own spiking history and the concurrent
activity of simultaneously recorded neurons. Granger causality is assessed based on the relative reduction of the point
process likelihood of one neuron obtained excluding one of its covariates compared to the likelihood obtained using all of
its covariates. The method was tested on simulated data, and then applied to neural activity recorded from the primary
motor cortex (MI) of a Felis catus subject. The interactions present in the simulated data were predicted with a high degree
of accuracy, and when applied to the real neural data, the proposed method identified causal relationships between many
of the recorded neurons. This paper proposes a novel method that successfully applies Granger causality to point process
data, and has the potential to provide unique physiological insights when applied to neural spike trains.National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant R01-EB006385
A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data
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 L penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Point process modeling as a framework to dissociate intrinsic and extrinsic components in neural systems
Understanding the factors shaping neuronal spiking is a central problem in neuroscience. Neurons may have complicated sensitivity and, often, are embedded in dynamic networks whose ongoing activity may influence their likelihood of spiking. One approach to characterizing neuronal spiking is the point process generalized linear model (GLM), which decomposes spike probability into explicit factors. This model represents a higher level of abstraction than biophysical models, such as Hodgkin-Huxley, but benefits from principled approaches for estimation and validation.
Here we address how to infer factors affecting neuronal spiking in different types of neural systems. We first extend the point process GLM, most commonly used to analyze single neurons, to model population-level voltage discharges recorded during human seizures. Both GLMs and descriptive measures reveal rhythmic bursting and directional wave propagation. However, we show that GLM estimates account for covariance between these features in a way that pairwise measures do not. Failure to account for this covariance leads to confounded results. We interpret the GLM results to speculate the mechanisms of seizure and suggest new therapies.
The second chapter highlights flexibility of the GLM. We use this single framework to analyze enhancement, a statistical phenomenon, in three distinct systems. Here we define the enhancement score, a simple measure of shared information between spike factors in a GLM. We demonstrate how to estimate the score, including confidence intervals, using simulated data. In real data, we find that enhancement occurs prominently during human seizure, while redundancy tends to occur in mouse auditory networks. We discuss implications for physiology, particularly during seizure.
In the third part of this thesis, we apply point process modeling to spike trains recorded from single units in vitro under external stimulation. We re-parameterize models in a low-dimensional and physically interpretable way; namely, we represent their effects in principal component space. We show that this approach successfully separates the neurons observed in vitro into different classes consistent with their gene expression profiles.
Taken together, this work contributes a statistical framework for analyzing neuronal spike trains and demonstrates how it can be applied to create new insights into clinical and experimental data sets
Model-free reconstruction of neuronal network connectivity from calcium imaging signals
A systematic assessment of global neural network connectivity through direct
electrophysiological assays has remained technically unfeasible even in
dissociated neuronal cultures. We introduce an improved algorithmic approach
based on Transfer Entropy to reconstruct approximations to network structural
connectivities from network activity monitored through calcium fluorescence
imaging. Based on information theory, our method requires no prior assumptions
on the statistics of neuronal firing and neuronal connections. The performance
of our algorithm is benchmarked on surrogate time-series of calcium
fluorescence generated by the simulated dynamics of a network with known
ground-truth topology. We find that the effective network topology revealed by
Transfer Entropy depends qualitatively on the time-dependent dynamic state of
the network (e.g., bursting or non-bursting). We thus demonstrate how
conditioning with respect to the global mean activity improves the performance
of our method. [...] Compared to other reconstruction strategies such as
cross-correlation or Granger Causality methods, our method based on improved
Transfer Entropy is remarkably more accurate. In particular, it provides a good
reconstruction of the network clustering coefficient, allowing to discriminate
between weakly or strongly clustered topologies, whereas on the other hand an
approach based on cross-correlations would invariantly detect artificially high
levels of clustering. Finally, we present the applicability of our method to
real recordings of in vitro cortical cultures. We demonstrate that these
networks are characterized by an elevated level of clustering compared to a
random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted
for publicatio
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