2,203 research outputs found
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
Training deep neural density estimators to identify mechanistic models of neural dynamics
Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics
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
Inferring brain-wide interactions using data-constrained recurrent neural network models
Behavior arises from the coordinated activity of numerous anatomically and functionally distinct brain regions. Modern experimental tools allow unprecedented access to large neural populations spanning many interacting regions brain-wide. Yet, understanding such large-scale datasets necessitates both scalable computational models to extract meaningful features of inter-region communication and principled theories to interpret those features. Here, we introduce Current-Based Decomposition (CURBD), an approach for inferring brain-wide interactions using data-constrained recurrent neural network models that directly reproduce experimentally-obtained neural data. CURBD leverages the functional interactions inferred by such models to reveal directional currents between multiple brain regions. We first show that CURBD accurately isolates inter-region currents in simulated networks with known dynamics. We then apply CURBD to multi-region neural recordings obtained from mice during running, macaques during Pavlovian conditioning, and humans during memory retrieval to demonstrate the widespread applicability of CURBD to untangle brain-wide interactions underlying behavior from a variety of neural datasets
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
Investigating Information Flows in Spiking Neural Networks With High Fidelity
The brains of many organisms are capable of a wide variety of complex computations. This capability must be undergirded by a more general purpose computational capacity. The exact nature of this capacity, how it is distributed across the brains of organisms and how it arises throughout the course of development is an open topic of scientific investigation.
Individual neurons are widely considered to be the fundamental computational units of brains. Moreover, the finest scale at which large scale recordings of brain activity can be performed is the spiking activity of neurons and our ability to perform these recordings over large numbers of neurons and with fine spatial resolution is increasing rapidly. This makes the spiking activity of individual neurons a highly attractive data modality on which to study neural computation.
The framework of information dynamics has proven to be a successful approach towards interrogating the capacity for general purpose computation. It does this by revealing the atomic information processing operations of information storage, transfer and modification. Unfortunately, the study of information flows and other information processing operations from the spiking activity of neurons has been severely hindered by the lack of effective tools for estimating these quantities on this data modality. This thesis remedies this situation by presenting an estimator for information flows, as measured by Transfer Entropy (TE), that operates in continuous time on event-based data such as spike trains. Unlike the previous approach to the estimation of this quantity, which discretised the process into time bins, this estimator operates on the raw inter-spike intervals. It is demonstrated to be far superior to the previous discrete-time approach in terms of consistency, rate of convergence and bias. Most importantly, unlike the discrete-time approach, which requires a hard tradeoff between capturing fine temporal precision or history effects occurring over reasonable time intervals, this estimator can capture history effects occurring over relatively large intervals without any loss of temporal precision.
This estimator is applied to developing dissociated cultures of cortical rat neurons, therefore providing the first high-fidelity study of information flows on spiking data. It is found that the spatial structure of the flows locks in to a significant extent. at the point of their emergence and that certain nodes occupy specialised computational roles as either transmitters, receivers or mediators of information flow. Moreover, these roles are also found to lock in early.
In order to fully understand the structure of neural information flows, however, we are required to go beyond pairwise interactions, and indeed multivariate information flows have become an important tool in the inference of effective networks from neuroscience data. These are directed networks where each node is connected to a minimal set of sources which maximally reduce the uncertainty in its present state. However, the application of multivariate information flows to the inference of effective networks from spiking data has been hampered by the above-mentioned issues with preexisting estimation techniques. Here, a greedy algorithm which iteratively builds a set of parents for each target node using multivariate transfer entropies, and which has already been well validated in the context of traditional discretely sampled time series, is adapted to use in conjunction with the newly developed estimator for event-based data. The combination of the greedy algorithm and continuous-time estimator is then validated on simulated examples for which the ground truth is known.
The new capabilities in the estimation of information flows and the inference of effective networks on event-based data presented in this work represent a very substantial step forward in our ability to perform these analyses on the ever growing set of high resolution, large scale recordings of interacting neurons. As such, this work promises to enable substantial quantitative insights in the future regarding how neurons interact, how they process information, and how this changes under different conditions such as disease
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