Circumstantial evidence and explanatory models for synapses in large-scale spike recordings

The simultaneous recording of the activity of many neurons poses challenges for multivariate data analysis. Here, we propose a general scheme of reconstruction of the functional network from spike train recordings. Effective, causal interactions are estimated by fitting generalized linear models on the neural responses, incorporating effects of the neurons’ self-history, of input from other neurons in the recorded network and of modulation by an external stimulus. The coupling terms arising from synaptic input can be transformed by thresholding into a binary connectivity matrix which is directed. Each link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. The resulting graph is analyzed with respect to small-world and scale-free properties using quantitative measures for directed networks. Such graph-theoretic analyses have been performed on many complex dynamic networks, including the connectivity structure between different brain areas. Only few studies have attempted to look at the structure of cortical neural networks on the level of individual neurons. Here, using multi-electrode recordings from the visual system of the awake monkey, we find that cortical networks lack scale-free behavior, but show a small, but significant small-world structure. Assuming a simple distance-dependent probabilistic wiring between neurons, we find that this connectivity structure can account for all of the networks’ observed small-world ness. Moreover, for multi-electrode recordings the sampling of neurons is not uniform across the population. We show that the small-world-ness obtained by such a localized sub-sampling overestimates the strength of the true small-world structure of the network. This bias is likely to be present in all previous experiments based on multi-electrode recordings.

Detecting synaptic connections using large-scale extracellular spike recordings presents a statistical challenge. Although previous methods often treat the detection of each putative connection as a separate hypothesis test, here we develop a modeling approach that infers synaptic connections while incorporating circuit properties learned from the whole network. We use an extension of the generalized linear model framework to describe the cross-correlograms between pairs of neurons and separate correlograms into two parts: a slowly varying effect due to background fluctuations and a fast, transient effect due to the synapse. We then use the observations from all putative connections in the recording to estimate two network properties: the presynaptic neuron type (excitatory or inhibitory) and the relationship between synaptic latency and distance between neurons. Constraining the presynaptic neuron's type, synaptic latencies, and time constants improves synapse detection. In data from simulated networks, this model outperforms two previously developed synapse detection methods, especially on the weak connections. We also apply our model to in vitro multielectrode array recordings from the mouse somatosensory cortex. Here, our model automatically recovers plausible connections from hundreds of neurons, and the properties of the putative connections are largely consistent with previous research.NEW & NOTEWORTHY Detecting synaptic connections using large-scale extracellular spike recordings is a difficult statistical problem. Here, we develop an extension of a generalized linear model that explicitly separates fast synaptic effects and slow background fluctuations in cross-correlograms between pairs of neurons while incorporating circuit properties learned from the whole network. This model outperforms two previously developed synapse detection methods in the simulated networks and recovers plausible connections from hundreds of neurons in in vitro multielectrode array data.

A fundamental challenge in neuroscience is to understand how decisions are computed in neural circuits. One popular approach to this problem is to record from single neurons in brain regions that lie between primary sensory and motor regions while an animal performs a perceptual decision-making task. Typical tasks require the animal to integrate noisy sensory evidence over time in order to make a binary decision about the stimulus. Such experiments have the tacit goal of characterizing the dynamics governing the transformation of sensory information into a representation of the decision. However, recorded spike trains do not reveal these dynamics directly; they represent noisy, incomplete emissions that reflect the underlying dynamics only indirectly.

Event Abstract Back to Event TOOLCONNECT: A powerful toolbox for functional connectivity analysis of in vitro neural networks Vito P. Pastore1*, Aleksandar Godjoski1, Sergio Martinoia1 and Paolo Massobrio1 1 University of Genova, Department of Informatics, Bioengineering, Robotics, System Engineering , Italy Motivation One of the goal of contemporary neuroscience is to study the interplay between topology, structure, functional-effective connectivity and neuronal dynamics at different level of complexity and on different experimental models (from simple in-vitro networks to whole brain areas). Functional connectivity is defined as the strength of the influence one network member has on another during ongoing behavior [1]. The analysis of multiple neural spike train data recorded from experimental models has gained tremendous relevance recently with the widespread application of Micro-Electrode Arrays (MEAs) [2]. At present, to the best of our knowledge, there is no available dedicated software that puts together a set of different functional connectivity analysis methods. Thus, we developed a user-friendly toolbox [3] in order to provide the researchers community a powerful tool to perform functional connectivity analysis on in-vitro neuronal networks coupled to standard and high-density MEAs, while guaranteeing computational efficiency and high accuracy. Material and Methods We implemented 'ToolConnect' toolbox as a standalone windows Graphical User Interface (GUI) application, using C# and Microsoft Visual Studio with .NET framework 4.5 development environment. The software is designed to be intuitive and straightforward to use. It is based on several windows forms and a friendly and modular GUI through which provides the user with powerful tools to manipulate and analyze data. ToolConnect offers functional connectivity analysis based on two correlation (cross-correlation and partial correlation) and two information theory based methods (transfer entropy and joint entropy). Cross correlation measures the frequency at which one cell fires as a function of time relative to the firing of a spike in another cell [4]. Partial correlation allows to distinguish between direct and indirect connections by removing the portion of the relationship between two spike trains that can be attributed to linear relationships with recorded spike trains from other neurons [5, 6]. Transfer Entropy is an information theoretic measure able to estimate causal relationships between time series taking into account their past activity [7]. Joint Entropy analyzes the cross Inter-Spike-Intervals (cISI): if two neurons are strongly connected the cISI histogram will show a peak and Joint Entropy will be close to zero, otherwise the cISI histogram will be almost flat, and the Joint Entropy will be high. The graphical section offers dedicated interfaces and allows the user to: i) plot the correlograms between each couple of the set of analyzed electrodes (for cross- and partial correlation); ii) manage, thresh and plot the Connectivity Matrix (CM) and the connectivity graph; iii) compute some powerful metrics that allow to extract the main topological features (degree, cluster coefficient, path length). One of the major features of the toolbox is its independence from the acquisition system (e.g. Multi Channel Systems, Qwane Biosciences, 3Brain) and from the MEA layout (number of microelectrodes and spatial organization). Results We designed and developed ToolConnect taking care to satisfy the user-friendliness requirement. According to this, our software has a GUI, which permits also to inexperienced users to perform functional connectivity analysis, to graphically represent the results, hiding the algorithms implementation specifics and software’s code design. Figure 1 shows a screenshot of ToolConnect’s GUI. Figure 2 shows the connectivity graphs obtained from the analysis of cortical networks coupled to the MEA60 and the MEA2100 acquisition systems of Multi Channel Systems (www.multichannelsystems.com; MCS, Reutlingen, Germany) and the BioCam acquisition system of 3Brain Systems. To assess the performances of tool connect we performed functional-connectivity analysis based on the cross-correlation method on hippocampal neuronal networks coupled to the MEA 60 from Multi-Channel Systems (MCS), during spontaneous and stimulus-evoked activity[3]. Discussion To the best of our knowledge, ToolConnect is the first functional connectivity toolbox dedicated to the analysis of multiple spike trains recorded from in-vitro neural networks coupled to MEAs. It provides the user with a complete set of computational and graphical tools of intuitive and straightforward usage through a dedicated and modular GUI. ToolConnect is implemented taking care of the optimization of the resources usage (requested RAM) and the reduction of the computational time. We were able to obtain acceptable performances with computational time lower than 2 minutes (for 10 minutes of recording sampled at 10 kHz). These performances make ToolConnect compatible with high-density recording systems (e.g., the 4096 electrodes of the 3brain system). In this way, it will be possible to perform functional connectivity analysis on neural networks with dimensions of thousands of neurons preserving an acceptable spatial and temporal resolution, hence allowing to obtain realistic and complete information on the dynamics and the topology of such systems.

The firing of neurons is studied via recorded spike trains. A technique for estimating the summation function, the decay function and the firing probability function of a neuron model, on the basis of recorded output and corresponding input spike trains, is described and illustrated for the neuron L3 of Aplysia californica firing under the influence of the neuron L10. The procedure of employing partial coherences to “remove” the effects of a common stimulation on pairs of neurons is validated by applying the technique to neurons of the cat’s auditory thalam us. In this case, the data were collected for the neurons firing first in a spontaneous fashion and then in response to stimulation. Finally coherences within groups of eight neurons are averaged together on the basis of known anatomy to enhance discernment of patterns. In some cases, significant peaks were found in partial coherences where no signs of association were observed during spontaneous firing. It is concluded that the techniques presented here provide a valuable improvement in detecting associations between neurons which are modulated by a stimulus, but are not necessarily time-locked to its time course.

Uncovering the causal relationship between spike train recordings from different neurons is a key issue for understanding the neural coding. This chapter presents a method, called permutation conditional mutual information (PCMI), for characterizing the causality between a pair of neurons. The performance of this method is demonstrated with the spike trains generated by the Izhikevich neuronal model, including estimation of the directionality index and detection of the temporal dynamics of the causal link. Simulations show that the PCMI method is superior to the transfer entropy (TE) and causal entropy (CE) methods at identifying the coupling direction between the spike trains. The advantages of PCMI are twofold: it is able to estimate the directionality index under the weak coupling and against the missing and extra spikes.

Uncovering the causal relationship between spike train recordings from different neurons is a key issue for understanding the neural coding. This paper presents a method, called permutation conditional mutual information (PCMI), for characterizing the causality between a pair of neurons. The performance of this method is demonstrated with the spike trains generated by the Poisson point process model and the Izhikevich neuronal model, including estimation of the directionality index and detection of the temporal dynamics of the causal link. Simulations show that the PCMI method is superior to the transfer entropy and causal entropy methods at identifying the coupling direction between the spike trains. The advantages of PCMI are twofold: It is able to estimate the directionality index under the weak coupling and against the missing and extra spikes.

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Estimating the causal interaction between neurons is very important for better understanding the functional connectivity in neuronal networks. We propose a method called normalized permutation transfer entropy (NPTE) to evaluate the temporal causal interaction between spike trains, which quantifies the fraction of ordinal information in a neuron that has presented in another one. The performance of this method is evaluated with the spike trains generated by an Izhikevich’s neuronal model. Results show that the NPTE method can effectively estimate the causal interaction between two neurons without influence of data length. Considering both the precision of time delay estimated and the robustness of information flow estimated against neuronal firing rate, the NPTE method is superior to other information theoretic method including normalized transfer entropy, symbolic transfer entropy and permutation conditional mutual information. To test the performance of NPTE on analyzing simulated biophysically realistic synapses, an Izhikevich’s cortical network that based on the neuronal model is employed. It is found that the NPTE method is able to characterize mutual interactions and identify spurious causality in a network of three neurons exactly. We conclude that the proposed method can obtain more reliable comparison of interactions between different pairs of neurons and is a promising tool to uncover more details on the neural coding.

Structural plasticity governs the long-term development of synaptic connections in the neocortex. While the underlying processes at the synapses are not fully understood, there is strong evidence that a process of random, independent formation and pruning of excitatory synapses can be ruled out. Instead, there must be some cooperation between the synaptic contacts connecting a single pre- and postsynaptic neuron pair. So far, the mechanism of cooperation is not known. Here we demonstrate that local correlation detection at the postsynaptic dendritic spine suffices to explain the synaptic cooperation effect, without assuming any hypothetical direct interaction pathway between the synaptic contacts. Candidate biomolecular mechanisms for dendritic correlation detection have been identified previously, as well as for structural plasticity based thereon. By analyzing and fitting of a simple model, we show that spike-timing correlation dependent structural plasticity, without additional mechanisms of cross-synapse interaction, can reproduce the experimentally observed distributions of numbers of synaptic contacts between pairs of neurons in the neocortex. Furthermore, the model yields a first explanation for the existence of both transient and persistent dendritic spines and allows to make predictions for future experiments.

Brain oscillations are thought to subserve important functions by organizing the dynamical landscape of neural circuits. The expression of such oscillations in neural signals is usually evaluated using time-frequency representations (TFR), which resolve oscillatory processes in both time and frequency. While a vast number of methods exist to compute TFRs, there is often no objective criterion to decide which one is better. In feature-rich data, such as that recorded from the brain, sources of noise and unrelated processes abound and contaminate results. The impact of these distractor sources is especially problematic, such that TFRs that are more robust to contaminants are expected to provide more useful representations. In addition, the minutiae of the techniques themselves impart better or worse time and frequency resolutions, which also influence the usefulness of the TFRs. Here, we introduce a methodology to evaluate the “quality” of TFRs of neural signals by quantifying how much information they retain about the experimental condition during visual stimulation and recognition tasks, in mice and humans, respectively. We used machine learning to discriminate between various experimental conditions based on TFRs computed with different methods. We found that various methods provide more or less informative TFRs depending on the characteristics of the data. In general, however, more advanced techniques, such as the superlet transform, seem to provide better results for complex time-frequency landscapes, such as those extracted from electroencephalography signals. Finally, we introduce a method based on feature perturbation that is able to quantify how much time-frequency components contribute to the correct discrimination among experimental conditions. The methodology introduced in the present study may be extended to other analyses of neural data, enabling the discovery of data features that are modulated by the experimental manipulation.

Consistency between Direct and Indirect Trial Evidence: Is Direct Evidence Always More Reliable?

Event Abstract Back to Event Neuron versus Time Clustering in the Identification of Cell Assemblies Carlos Toledo-Suárez1, 2, 3*, Man Yi Yim1, 4, Arvind Kumar1, 4 and Abigail Morrison1, 2 1 University of Freiburg, Germany 2 University of Freiburg, Faculty of Biology, Germany 3 School of Computer Science and Communication, KTH, Computational Biology, Sweden 4 University of Freiburg, Faculty of Biology, Germany A major challenge in the analysis of neural activity data when considering spikes as the main information carrying unit is the detection of sets of neurons which act as functional groups. Such neuronal cell assemblies can be identified by clustering the spectrum of zero-lag cross-correlation between all pairs of neurons in a network or by dimensionality reduction of the similarity matrix of the spike trains. Here we investigate how the identification of cell assemblies is dependent on the methodology chosen. We construct a self similar network of inhibitory adaptive exponential integrate-and-fire neurons that is stimulated with Poissonian excitatory input. For such a network one would expect that groups of neurons show a similar activity as the network as a whole. However, we observe that there is a difference between the evolution of network activity and sets of neurons clustered according to their correlation. When analyzing medium spiny neuron calcium imaging data, we again find that the results of the two methods are not in line. Acknowledgements Partially funded by the German Federal Ministry of Education and Research (BMBF 01GQ0420 to BCCN Freiburg, BMBF GW0542 Cognition and BMBF 01GW0730 Impulse Control), EU Grant 269921 (BrainScaleS), Helmholtz Alliance on Systems Biology (Germany), Neurex, the the Junior Professor Program of Baden-Württemberg and the Erasmus Mundus Joint Doctoral programme EuroSPIN.

To assess temporal associations in spike activity between pairs of neurons in the primary motor cortex (MI) related to different behaviors, we compared the incidence of coincident spiking activity of task-related (TR) and non-task-related (NTR) neurons during a skilled motor task and sitting quietly in adult cats (Felis domestica). Chronically implanted microwires were used to record spike activity of MI neurons in four animals (two male and two female) trained to perform a skilled reaching task or sit quietly. Neurons were identified as TR if spike activity was modulated during the task (and NTR if not). Based on spike characteristics, they were also classified as either regular-spiking (RS, putatively excitatory) or fast-spiking (FS, putatively inhibitory) neurons. Temporal associations in the activities of simultaneously recorded neurons were evaluated using shuffle-corrected cross-correlograms. Pairs of NTR and TR neurons showed associations in their firing patterns over wide areas of MI (representing forelimb and hindlimb movements) during quiet sitting, more commonly involving RS neurons. During skilled task performance, however, significantly coincident firing was seen almost exclusively between TR neurons in a smaller part of MI (representing forelimb movements), involving mainly FS neurons. The findings of this study show evidence for widespread interactions in MI when the animal sits quietly, which changes to a more specific and restricted pattern of interactions during task performance. Different populations of excitatory and inhibitory neurons appear to be synchronized during skilled movement and quiet sitting.

A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the "inputs" and "outputs", respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The "scaling-up" issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.