Statistical technique for analysing functional connectivity of multiple spike trains

Local Independence Testing for Point Processes

Constraint-based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g., that the true data generating model is a Hawkes process with no latent confounders. Even when restricting attention to Hawkes processes, latent confounders are a major technical difficulty because a marginalized process will generally not be a Hawkes process itself. We introduce an expansion similar to Volterra expansions as a tool to represent marginalized intensities. Our main theoretical result is that such expansions can approximate the true marginalized intensity arbitrarily well. Based on this, we propose a test of local independence and investigate its properties in real and simulated data.

Discovering Effective Connectivity in Neural Circuits: Analysis Based on Machine Learning Methodology

As multielectrode array technology increases in popularity, accessible analytical tools become necessary. Simultaneous recordings from multiple neurons may produce huge amounts of information. Traditional tools based on classical statistics are either insufficient to analyze multiple spike trains or sophisticated and expensive in computing terms. In this communication, we put to the test the idea that AI algorithms may be useful to gather information about the effective connectivity of neurons in local nuclei at a relatively low computing cost. To this end, we decided to explore the capacity of the algorithm C5.0 to retrieve information from a large series of spike trains obtained from a simulated neuronal circuit with a known structure. Combinatory, iterative and recursive processes using C5.0 were built to examine possibilities of increasing the performance of a direct application of the algorithm. Furthermore, we tested the applicability of these processes to a reduced dataset obtained from original biological recordings with unknown connectivity. This was obtained in house from a mouse in vitro preparation of the spinal cord. Results show that this algorithm can retrieve neurons monosynaptically connected to the target in simulated datasets within a single run. Iterative and recursive processes can identify monosynaptic neurons and disynaptic neurons under favorable conditions. Application of these processes to the biological dataset gives clues to identify neurons monosynaptically connected to the target. We conclude that the work presented provides substantial proof of concept for the potential use of AI algorithms to the study of effective connectivity.

Inhibitory interneurons in a brainstem circuit adjust their inhibitory motifs to process multimodal input

KEY POINTS

Inhibitory-interneuron networks, consisting of multiple forms of circuit motifs including reciprocal (inhibitory interneurons inhibiting other interneurons) and feedforward (inhibitory interneurons inhibiting principal neurons) connections, are crucial in processing sensory information. The present study applies a statistical method to in vivo multichannel spike trains of dorsal cochlear nucleus neurons to disentangle reciprocal and feedforward-inhibitory motifs. After inducing input-specific plasticity, reciprocal and feedforward inhibition are found to be differentially regulated, and the combined effect synergistically modulates circuit output. The findings highlight the interplay among different circuit motifs as a key element in neural computation.

ABSTRACT

Inhibitory interneurons play an essential role in neural computations by utilizing a combination of reciprocal (interneurons inhibiting each other) and feedforward (interneuron inhibiting the principal neuron) inhibition to process information. To disentangle the interplay between the two inhibitory-circuit motifs and understand their effects on the circuit output, in vivo recordings were made from the guinea pig dorsal cochlear nucleus, a cerebellar-like brainstem circuit. Spikes from inhibitory interneurons (cartwheel cell) and principal output neurons (fusiform cell) were compared before and after manipulating their common multimodal input. Using a statistical model based on the Cox method of modulated renewal process of spike train influence, reciprocal- and feedforward-inhibition motifs were quantified. In response to altered multimodal input, reciprocal inhibition was strengthened while feedforward inhibition was weakened, and the two motifs combined to modulate fusiform cell output and acoustic-driven responses. These findings reveal the cartwheel cell's role in auditory and multimodal processing, as well as illustrated the balance between different inhibitory-circuit motifs as a key element in neural computation.

A study of dependency features of spike trains through copulas

Despite the progresses of statistical and machine learning techniques, simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered. Discerning the presence of direct links between neurons from data is still a not completely solved problem. We propose the use of copulas, to enlarge the number of tools for detecting the network structure, pursuing on a research direction we started in Sacerdote et al. (2012). Here, our aim is to distinguish different types of connections on a very simple network. Our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. We show that this approach allows to detect different types of dependencies. We illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. We show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and indirect interactions.

Learning High-dimensional Generalized Linear Autoregressive Models

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregressive model would correspond to the impact of the network structure on the time series evolution. Often these models are used successfully in practice to learn the structure of social, epidemiological, financial, or biological neural networks. However, little is known about statistical guarantees on estimates of such models in non-Gaussian settings. This paper addresses the inference of the autoregressive parameters and associated network structure within a generalized linear model framework that includes Poisson and Bernoulli autoregressive processes. At the heart of this analysis is a sparsity-regularized maximum likelihood estimator. While sparsity-regularization is well-studied in the statistics and machine learning communities, those analysis methods cannot be applied to autoregressive generalized linear models because of the correlations and potential heteroscedasticity inherent in the observations. Sample complexity bounds are derived using a combination of martingale concentration inequalities and modern empirical process techniques for dependent random variables. These bounds, which are supported by several simulation studies, characterize the impact of various network parameters on estimator performance.

Reconstructing the functional connectivity of multiple spike trains using Hawkes models

BACKGROUND

Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation.

NEW METHOD

Here, we present a method, based on least-square estimators and LASSO penalty criteria, for a particular class of Hawkes processes that can be used for simulation.

RESULTS

Testing our method on small networks modeled with Leaky Integrate and Fire demonstrated that it efficiently detects both excitatory and inhibitory connections. The few errors that occasionally occur with complex networks including common inputs, weak and chained connections, can be discarded based on objective criteria.

COMPARISON WITH EXISTING METHODS

With respect to other existing methods, the present one allows to reconstruct functional connectivity of small networks without prior knowledge of their properties or architecture, using an experimentally realistic amount of data.

CONCLUSIONS

The present method is robust, stable, and can be used on a personal computer as a routine procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings.

Adaptive filtering for hidden node detection and tracking in networks

The identification of network connectivity from noisy time series is of great interest in the study of network dynamics. This connectivity estimation problem becomes more complicated when we consider the possibility of hidden nodes within the network. These hidden nodes act as unknown drivers on our network and their presence can lead to the identification of false connections, resulting in incorrect network inference. Detecting the parts of the network they are acting on is thus critical. Here, we propose a novel method for hidden node detection based on an adaptive filtering framework with specific application to neuronal networks. We consider the hidden node as a problem of missing variables when model fitting and show that the estimated system noise covariance provided by the adaptive filter can be used to localize the influence of the hidden nodes and distinguish the effects of different hidden nodes. Additionally, we show that the sequential nature of our algorithm allows for tracking changes in the hidden node influence over time.

Correlations and Neuronal Population Information

Brain function involves the activity of neuronal populations. Much recent effort has been devoted to measuring the activity of neuronal populations in different parts of the brain under various experimental conditions. Population activity patterns contain rich structure, yet many studies have focused on measuring pairwise relationships between members of a larger population-termed noise correlations. Here we review recent progress in understanding how these correlations affect population information, how information should be quantified, and what mechanisms may give rise to correlations. As population coding theory has improved, it has made clear that some forms of correlation are more important for information than others. We argue that this is a critical lesson for those interested in neuronal population responses more generally: Descriptions of population responses should be motivated by and linked to well-specified function. Within this context, we offer suggestions of where current theoretical frameworks fall short.

Time-Dependent Increase in Network Response to Stimulation

In vitro neuronal cultures have become a popular method with which to probe network-level neuronal dynamics and phenomena in controlled laboratory settings. One of the key dynamics of interest in these in vitro studies has been the extent to which cultured networks display properties indicative of learning. Here we demonstrate the effects of a high frequency electrical stimulation signal in training cultured networks of cortical neurons. Networks receiving this training signal displayed a time-dependent increase in the response to a low frequency probing stimulation, particularly in the time window of 20–50 ms after stimulation. This increase was found to be statistically significant as compared to control networks that did not receive training. The timing of this increase suggests potentiation of synaptic mechanisms. To further investigate this possibility, we leveraged the powerful Cox statistical connectivity method as previously investigated by our group. This method was used to identify and track changes in network connectivity strength.

A Digital Repository and Execution Platform for Interactive Scholarly Publications in Neuroscience

The CARMEN Virtual Laboratory (VL) is a cloud-based platform which allows neuroscientists to store, share, develop, execute, reproduce and publicise their work. This paper describes new functionality in the CARMEN VL: an interactive publications repository. This new facility allows users to link data and software to publications. This enables other users to examine data and software associated with the publication and execute the associated software within the VL using the same data as the authors used in the publication. The cloud-based architecture and SaaS (Software as a Service) framework allows vast data sets to be uploaded and analysed using software services. Thus, this new interactive publications facility allows others to build on research results through reuse. This aligns with recent developments by funding agencies, institutions, and publishers with a move to open access research. Open access provides reproducibility and verification of research resources and results. Publications and their associated data and software will be assured of long-term preservation and curation in the repository. Further, analysing research data and the evaluations described in publications frequently requires a number of execution stages many of which are iterative. The VL provides a scientific workflow environment to combine software services into a processing tree. These workflows can also be associated with publications and executed by users. The VL also provides a secure environment where users can decide the access rights for each resource to ensure copyright and privacy restrictions are met.

Functional connectivity changes during a working memory task in rat via NMF analysis

Working memory (WM) is necessary in higher cognition. The brain as a complex network is formed by interconnections among neurons. Connectivity results in neural dynamics to support cognition. The first aim is to investigate connectivity dynamics in medial prefrontal cortex (mPFC) networks during WM. As brain neural activity is sparse, the second aim is to find the intrinsic connectivity property in a feature space. Using multi-channel electrode recording techniques, spikes were simultaneously obtained from mPFC of rats that performed a Y-maze WM task. Continuous time series converted from spikes were embedded in a low-dimensional space by non-negative matrix factorization (NMF). mPFC network in original space was constructed by measuring connections among neurons. And the same network in NMF space was constructed by computing connectivity values between the extracted NMF components. Causal density (Cd) and global efficiency (E) were estimated to present the network property. The results showed that Cd and E significantly peaked in the interval right before the maze choice point in correct trials. However, the increase did not emerge in error trials. Additionally, Cd and E in two spaces displayed similar trends in correct trials. The difference was that the measures in NMF space were significantly greater than those in original space. Our findings indicated that the anticipatory changes in mPFC networks may have an effect on future WM behavioral choices. Moreover, the NMF analysis achieves a better characterization for a brain network.

Real-time tracking of neuronal network structure using data assimilation

A nonlinear data assimilation technique is applied to determine and track effective connections between ensembles of cultured spinal cord neurons measured with multielectrode arrays. The method is statistical, depending only on confidence intervals, and requiring no form of arbitrary thresholding. In addition, the method updates connection strengths sequentially, enabling real-time tracking of nonstationary networks. The ensemble Kalman filter is used with a generic spiking neuron model to estimate connection strengths as well as other system parameters to deal with model mismatch. The method is validated on noisy synthetic data from Hodgkin-Huxley model neurons before being used to find network connections in the neural culture recordings.

Statistical evaluation of synchronous spike patterns extracted by frequent item set mining

We recently proposed frequent itemset mining (FIM) as a method to perform an optimized search for patterns of synchronous spikes (item sets) in massively parallel spike trains. This search outputs the occurrence count (support) of individual patterns that are not trivially explained by the counts of any superset (closed frequent item sets). The number of patterns found by FIM makes direct statistical tests infeasible due to severe multiple testing. To overcome this issue, we proposed to test the significance not of individual patterns, but instead of their signatures, defined as the pairs of pattern size z and support c. Here, we derive in detail a statistical test for the significance of the signatures under the null hypothesis of full independence (pattern spectrum filtering, PSF) by means of surrogate data. As a result, injected spike patterns that mimic assembly activity are well detected, yielding a low false negative rate. However, this approach is prone to additionally classify patterns resulting from chance overlap of real assembly activity and background spiking as significant. These patterns represent false positives with respect to the null hypothesis of having one assembly of given signature embedded in otherwise independent spiking activity. We propose the additional method of pattern set reduction (PSR) to remove these false positives by conditional filtering. By employing stochastic simulations of parallel spike trains with correlated activity in form of injected spike synchrony in subsets of the neurons, we demonstrate for a range of parameter settings that the analysis scheme composed of FIM, PSF and PSR allows to reliably detect active assemblies in massively parallel spike trains.

The use of dendrograms to describe the electrical activity of motoneurons underlying behaviors in leeches

The present manuscript aims at identifying patterns of electrical activity recorded from neurons of the leech nervous system, characterizing specific behaviors. When leeches are at rest, the electrical activity of neurons and motoneurons is poorly correlated. When leeches move their head and/or tail, in contrast, action potential (AP) firing becomes highly correlated. When the head or tail suckers detach, specific patterns of electrical activity are detected. During elongation and contraction the electrical activity of motoneurons in the Medial Anterior and Dorsal Posterior nerves increase, respectively, and several motoneurons are activated both during elongation and contraction. During crawling, swimming, and pseudo-swimming patterns of electrical activity are better described by the dendrograms of cross-correlations of motoneurons pairs. Dendrograms obtained from different animals exhibiting the same behavior are similar and by averaging these dendrograms we obtained a template underlying a given behavior. By using this template, the corresponding behavior is reliably identified from the recorded electrical activity. The analysis of dendrograms during different leech behavior reveals the fine orchestration of motoneurons firing specific to each stereotyped behavior. Therefore, dendrograms capture the subtle changes in the correlation pattern of neuronal networks when they become involved in different tasks or functions.

Detecting connectivity changes in neuronal networks

We develop a method from semiparametric statistics (Cox, 1972) for the purpose of tracking links and connection strengths over time in a neuronal network from spike train data. We consider application of the method as implemented in Masud and Borisyuk (2011), and evaluate its use on data generated independently of the Cox model hypothesis, in particular from a spiking model of Izhikevich in four different dynamical regimes. Then, we show how the Cox method can be used to determine statistically significant changes in network connectivity over time. Our methodology is demonstrated using spike trains from multi-electrode array measurements of networks of cultured mammalian spinal cord cells.

Neuroplasticity of the sensorimotor cortex during learning

We will discuss some of the current issues in understanding plasticity in the sensorimotor (SM) cortices on the behavioral, neurophysiological, and synaptic levels. We will focus our paper on reaching and grasping movements in the rat. In addition, we will discuss our preliminary work utilizing inhibition of protein kinase Mζ (PKMζ), which has recently been shown necessary and sufficient for the maintenance of long-term potentiation (LTP) (Ling et al., 2002). With this new knowledge and inhibitors to this system, as well as the ability to overexpress this system, we can start to directly modulate LTP and determine its influence on behavior as well as network level processing dependent at least in part due to this form of LTP. We will also briefly introduce the use of brain machine interface (BMI) paradigms to ask questions about sensorimotor plasticity and discuss current analysis techniques that may help in our understanding of neuroplasticity.

Detecting dependencies between spike trains of pairs of neurons through copulas

The dynamics of a neuron are influenced by the connections with the network where it lies. Recorded spike trains exhibit patterns due to the interactions between neurons. However, the structure of the network is not known. A challenging task is to investigate it from the analysis of simultaneously recorded spike trains. We develop a non-parametric method based on copulas, that we apply to simulated data according to different bivariate Leaky Integrate and Fire models. The method discerns dependencies determined by the surrounding network, from those determined by direct interactions between the two neurons. Furthermore, the method recognizes the presence of delays in the spike propagation. This article is part of a Special Issue entitled "Neural Coding".

A new similarity measure for spike trains: sensitivity to bursts and periods of inhibition

An important problem in neuroscience is that of constructing quantitative measures of the similarity between neural spike trains. These measures can be used, for example, to assess the reliability of the response of a single neuron to repeated stimulus presentations, or to uncover relationships in the firing patterns of multiple neurons in a population. While several similarity measures have been proposed, the extent to which they take into account various biologically important spike train features such as bursts of spikes, or periods of inactivity remains poorly understood. Here we compare these measures using tests specifically designed to assess the sensitivity to bursts and silent periods. In addition, we propose two new measures. The first is designed to detect periods of shared silence between spike trains, while the second is designed to emphasize the presence of common bursts. To assist researchers in determining which measure is best suited to their particular data analysis needs, we also show how these measures can be combined and how their parameters can be determined on the basis of physiologically relevant quantities.