Using transfer entropy to study synaptic integration in Purkinje cells

Peer reviewe

Assessment of Effective Connectivity in Alzheimer’s Disease Using Granger Causality

Producción CientíficaAlzheimer’s disease (AD) is a neurological disorder accompanied by cognitive impairment. A complete understanding of the neurological processes involved in AD is a leading challenge in brain research. In this study, resting-state magnetoencephalography (MEG) activity from 36 AD patients and 26 healthy controls was evaluated by means of Granger Causality (GC), an effective connectivity measure that provides an estimation of the information flow between brain regions. Our results showed widespread increments in connectivity in delta (, 1-4 Hz) band. On the other hand, decrements in connectivity patterns were found for theta (, 4-8 Hz), beta (, 13-30 Hz), and gamma (, 30-65 Hz) bands. These findings strength the disconnection hypothesis in AD, and reveal GC as a useful parameter for AD identification.Ministerio de Economía y Competitividad (TEC2014-53196-R)Junta de Castilla y León (VA059U13 y BIO/VA08/15

Detection and localization of multiple rate changes in Poisson spike trains

Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. In statistical spike train analysis, stochastic point process models usually assume stationarity, in particular that the underlying spike train shows a constant firing rate (e.g. [1]). However, such models can lead to misinterpretation of the associated tests if the assumption of rate stationarity is not met (e.g. [2]). Therefore, the analysis of nonstationary data requires that rate changes can be located as precisely as possible. However, present statistical methods focus on rejecting the null hypothesis of stationarity without explicitly locating the change point(s) (e.g. [3]). We propose a test for stationarity of a given spike train that can also be used to estimate the change points in the firing rate. Assuming a Poisson process with piecewise constant firing rate, we propose a Step-Filter-Test (SFT) which can work simultaneously in different time scales, accounting for the high variety of firing patterns in experimental spike trains. Formally, we compare the numbers N1=N1(t,h) and N2=N2(t,h) of spikes in the time intervals (t-h,t] and (h,t+h]. By varying t within a fine time lattice and simultaneously varying the interval length h, we obtain a multivariate statistic D(h,t):=(N1-N2)/V(N1+N2), for which we prove asymptotic multivariate normality under homogeneity. From this a practical, graphical device to spot changes of the firing rate is constructed. Our graphical representation of D(h,t) (Figure 1A) visualizes the changes in the firing rate. For the statistical test, a threshold K is chosen such that under homogeneity, |D(h,t)|<K holds for all investigated h and t with probability 0.95. This threshold can indicate potential change points in order to estimate the inhomogeneous rate profile (Figure 1B). The SFT is applied to a sample data set of spontaneous single unit activity recorded from the substantia nigra of anesthetized mice. In this data set, multiple rate changes are identified which agree closely with visual inspection. In contrast to approaches choosing one fixed kernel width [4], our method has advantages in the flexibility of h

Beyond element-wise interactions: identifying complex interactions in biological processes

Background: Biological processes typically involve the interactions of a number of elements (genes, cells) acting on each others. Such processes are often modelled as networks whose nodes are the elements in question and edges pairwise relations between them (transcription, inhibition). But more often than not, elements actually work cooperatively or competitively to achieve a task. Or an element can act on the interaction between two others, as in the case of an enzyme controlling a reaction rate. We call “complex” these types of interaction and propose ways to identify them from time-series observations. Methodology: We use Granger Causality, a measure of the interaction between two signals, to characterize the influence of an enzyme on a reaction rate. We extend its traditional formulation to the case of multi-dimensional signals in order to capture group interactions, and not only element interactions. Our method is extensively tested on simulated data and applied to three biological datasets: microarray data of the Saccharomyces cerevisiae yeast, local field potential recordings of two brain areas and a metabolic reaction. Conclusions: Our results demonstrate that complex Granger causality can reveal new types of relation between signals and is particularly suited to biological data. Our approach raises some fundamental issues of the systems biology approach since finding all complex causalities (interactions) is an NP hard problem

Comparison of LFP-Based and Spike-Based Spectro-Temporal Receptive Fields and Cross-Correlation in Cat Primary Auditory Cortex

Multi-electrode array recordings of spike and local field potential (LFP) activity were made from primary auditory cortex of 12 normal hearing, ketamine-anesthetized cats. We evaluated 259 spectro-temporal receptive fields (STRFs) and 492 frequency-tuning curves (FTCs) based on LFPs and spikes simultaneously recorded on the same electrode. We compared their characteristic frequency (CF) gradients and their cross-correlation distances. The CF gradient for spike-based FTCs was about twice that for 2–40 Hz-filtered LFP-based FTCs, indicating greatly reduced frequency selectivity for LFPs. We also present comparisons for LFPs band-pass filtered between 4–8 Hz, 8–16 Hz and 16–40 Hz, with spike-based STRFs, on the basis of their marginal frequency distributions. We find on average a significantly larger correlation between the spike based marginal frequency distributions and those based on the 16–40 Hz filtered LFP, compared to those based on the 4–8 Hz, 8–16 Hz and 2–40 Hz filtered LFP. This suggests greater frequency specificity for the 16–40 Hz LFPs compared to those of lower frequency content. For spontaneous LFP and spike activity we evaluated 1373 pair correlations for pairs with >200 spikes in 900 s per electrode. Peak correlation-coefficient space constants were similar for the 2–40 Hz filtered LFP (5.5 mm) and the 16–40 Hz LFP (7.4 mm), whereas for spike-pair correlations it was about half that, at 3.2 mm. Comparing spike-pairs with 2–40 Hz (and 16–40 Hz) LFP-pair correlations showed that about 16% (9%) of the variance in the spike-pair correlations could be explained from LFP-pair correlations recorded on the same electrodes within the same electrode array. This larger correlation distance combined with the reduced CF gradient and much broader frequency selectivity suggests that LFPs are not a substitute for spike activity in primary auditory cortex

Evaluation of the Performance of Information Theory-Based Methods and Cross-Correlation to Estimate the Functional Connectivity in Cortical Networks

Functional connectivity of in vitro neuronal networks was estimated by applying different statistical algorithms on data collected by Micro-Electrode Arrays (MEAs). First we tested these “connectivity methods” on neuronal network models at an increasing level of complexity and evaluated the performance in terms of ROC (Receiver Operating Characteristic) and PPC (Positive Precision Curve), a new defined complementary method specifically developed for functional links identification. Then, the algorithms better estimated the actual connectivity of the network models, were used to extract functional connectivity from cultured cortical networks coupled to MEAs. Among the proposed approaches, Transfer Entropy and Joint-Entropy showed the best results suggesting those methods as good candidates to extract functional links in actual neuronal networks from multi-site recordings

Dynamic Effective Connectivity of Inter-Areal Brain Circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities

Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis

Characterizing how different cortical rhythms interact and how their interaction changes with sensory stimulation is important to gather insights into how these rhythms are generated and what sensory function they may play. Concepts from information theory, such as Transfer Entropy (TE), offer principled ways to quantify the amount of causation between different frequency bands of the signal recorded from extracellular electrodes; yet these techniques are hard to apply to real data. To address the above issues, in this study we develop a method to compute fast and reliably the amount of TE from experimental time series of extracellular potentials. The method consisted in adapting efficiently the calculation of TE to analog signals and in providing appropriate sampling bias corrections. We then used this method to quantify the strength and significance of causal interaction between frequency bands of field potentials and spikes recorded from primary visual cortex of anaesthetized macaques, both during spontaneous activity and during binocular presentation of naturalistic color movies. Causal interactions between different frequency bands were prominent when considering the signals at a fine (ms) temporal resolution, and happened with a very short (ms-scale) delay. The interactions were much less prominent and significant at coarser temporal resolutions. At high temporal resolution, we found strong bidirectional causal interactions between gamma-band (40–100 Hz) and slower field potentials when considering signals recorded within a distance of 2 mm. The interactions involving gamma bands signals were stronger during movie presentation than in absence of stimuli, suggesting a strong role of the gamma cycle in processing naturalistic stimuli. Moreover, the phase of gamma oscillations was playing a stronger role than their amplitude in increasing causations with slower field potentials and spikes during stimulation. The dominant direction of causality was mainly found in the direction from MUA or gamma frequency band signals to lower frequency signals, suggesting that hierarchical correlations between lower and higher frequency cortical rhythms are originated by the faster rhythms

Efficient Network Reconstruction from Dynamical Cascades Identifies Small-World Topology of Neuronal Avalanches

Cascading activity is commonly found in complex systems with directed interactions such as metabolic networks, neuronal networks, or disease spreading in social networks. Substantial insight into a system's organization can be obtained by reconstructing the underlying functional network architecture from the observed activity cascades. Here we focus on Bayesian approaches and reduce their computational demands by introducing the Iterative Bayesian (IB) and Posterior Weighted Averaging (PWA) methods. We introduce a special case of PWA, cast in nonparametric form, which we call the normalized count (NC) algorithm. NC efficiently reconstructs random and small-world functional network topologies and architectures from subcritical, critical, and supercritical cascading dynamics and yields significant improvements over commonly used correlation methods. With experimental data, NC identified a functional and structural small-world topology and its corresponding traffic in cortical networks with neuronal avalanche dynamics