Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Response inhibition in premotor cortex corresponds to a complex reshuffle of the mesoscopic information network

Recent studies have explored functional and effective neural networks in animal models; however, the dynamics of information propagation among functional modules under cognitive control remain largely unknown. Here, we addressed the issue using transfer entropy and graph theory methods on mesoscopic neural activities recorded in the dorsal premotor cortex of rhesus monkeys. We focused our study on the decision time of a Stop-signal task, looking for patterns in the network configuration that could influence motor plan maturation when the Stop signal is provided. When comparing trials with successful inhibition to those with generated movement, the nodes of the network resulted organized into four clusters, hierarchically arranged, and distinctly involved in information transfer. Interestingly, the hierarchies and the strength of information transmission between clusters varied throughout the task, distinguishing between generated movements and canceled ones and corresponding to measurable levels of network complexity. Our results suggest a putative mechanism for motor inhibition in premotor cortex: a topological reshuffle of the information exchanged among ensembles of neurons.

Integrated information decomposition unveils major structural traits of in silico and in vitro neuronal networks

The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behavior, it is crucial to convene as much information as possible about their topological organization. However, in large systems, such as neuronal networks, the reconstruction of such topology is usually carried out from the information encoded in the dynamics on the network, such as spike train time series, and by measuring the transfer entropy between system elements. The topological information recovered by these methods does not necessarily capture the connectivity layout, but rather the causal flow of information between elements. New theoretical frameworks, such as Integrated Information Decomposition (Φ-ID), allow one to explore the modes in which information can flow between parts of a system, opening a rich landscape of interactions between network topology, dynamics, and information. Here, we apply Φ-ID on in silico and in vitro data to decompose the usual transfer entropy measure into different modes of information transfer, namely, synergistic, redundant, or unique. We demonstrate that the unique information transfer is the most relevant measure to uncover structural topological details from network activity data, while redundant information only introduces residual information for this application. Although the retrieved network connectivity is still functional, it captures more details of the underlying structural topology by avoiding to take into account emergent high-order interactions and information redundancy between elements, which are important for the functional behavior, but mask the detection of direct simple interactions between elements constituted by the structural network topology.

Ensemble learning and ground-truth validation of synaptic connectivity inferred from spike trains

Probing the architecture of neuronal circuits and the principles that underlie their functional organization remains an important challenge of modern neurosciences. This holds true, in particular, for the inference of neuronal connectivity from large-scale extracellular recordings. Despite the popularity of this approach and a number of elaborate methods to reconstruct networks, the degree to which synaptic connections can be reconstructed from spike-train recordings alone remains controversial. Here, we provide a framework to probe and compare connectivity inference algorithms, using a combination of synthetic ground-truth and in vitro data sets, where the connectivity labels were obtained from simultaneous high-density microelectrode array (HD-MEA) and patch-clamp recordings. We find that reconstruction performance critically depends on the regularity of the recorded spontaneous activity, i.e., their dynamical regime, the type of connectivity, and the amount of available spike-train data. We therefore introduce an ensemble artificial neural network (eANN) to improve connectivity inference. We train the eANN on the validated outputs of six established inference algorithms and show how it improves network reconstruction accuracy and robustness. Overall, the eANN demonstrated strong performance across different dynamical regimes, worked well on smaller datasets, and improved the detection of synaptic connectivity, especially inhibitory connections. Results indicated that the eANN also improved the topological characterization of neuronal networks. The presented methodology contributes to advancing the performance of inference algorithms and facilitates our understanding of how neuronal activity relates to synaptic connectivity.

Common knowledge processing patterns in networks of different systems

Knowledge processing has patterns which can be found in biological neuron activity and artificial neural networks. The work explores whether an underlying structure exists for knowledge which crosses domains. The results show common data processing patterns in biological systems and human-made knowledge-based systems, present examples of human-generated knowledge processing systems, such as artificial neural networks and research topic knowledge networks, and explore change of system patterns over time. The work analyzes nature-based systems, which are animal connectomes, and observes neuron circuitry of knowledge processing based on complexity of the knowledge processing system. The variety of domains and similarity in processing mechanisms raise the question: if it is common in natural and artificial systems to see this pattern-based knowledge processing, how unique is knowledge processing in humans.

Analysis of functional connectivity using machine learning and deep learning in different data modalities from individuals with schizophrenia

Objective. Schizophrenia(SCZ) is a severe mental disorder associated with persistent or recurrent psychosis, hallucinations, delusions, and thought disorders that affect approximately 26 million people worldwide, according to the World Health Organization. Several studies encompass machine learning (ML) and deep learning algorithms to automate the diagnosis of this mental disorder. Others study SCZ brain networks to get new insights into the dynamics of information processing in individuals suffering from the condition. In this paper, we offer a rigorous approach with ML and deep learning techniques for evaluating connectivity matrices and measures of complex networks to establish an automated diagnosis and comprehend the topology and dynamics of brain networks in SCZ individuals.Approach.For this purpose, we employed an functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) dataset. In addition, we combined EEG measures, i.e. Hjorth mobility and complexity, with complex network measurements to be analyzed in our model for the first time in the literature.Main results.When comparing the SCZ group to the control group, we found a high positive correlation between the left superior parietal lobe and the left motor cortex and a positive correlation between the left dorsal posterior cingulate cortex and the left primary motor. Regarding complex network measures, the diameter, which corresponds to the longest shortest path length in a network, may be regarded as a biomarker because it is the most crucial measure in different data modalities. Furthermore, the SCZ brain networks exhibit less segregation and a lower distribution of information. As a result, EEG measures outperformed complex networks in capturing the brain alterations associated with SCZ.Significance. Our model achieved an area under receiver operating characteristic curve (AUC) of 100% and an accuracy of 98.5% for the fMRI, an AUC of 95%, and an accuracy of 95.4% for the EEG data set. These are excellent classification results. Furthermore, we investigated the impact of specific brain connections and network measures on these results, which helped us better describe changes in the diseased brain.

Neuronal Cultures: Exploring Biophysics, Complex Systems, and Medicine in a Dish

Neuronal cultures are one of the most important experimental models in modern interdisciplinary neuroscience, allowing to investigate in a control environment the emergence of complex behavior from an ensemble of interconnected neurons. Here, I review the research that we have conducted at the neurophysics laboratory at the University of Barcelona over the last 15 years, describing first the neuronal cultures that we prepare and the associated tools to acquire and analyze data, to next delve into the different research projects in which we actively participated to progress in the understanding of open questions, extend neuroscience research on new paradigms, and advance the treatment of neurological disorders. I finish the review by discussing the drawbacks and limitations of neuronal cultures, particularly in the context of brain-like models and biomedicine.

Archetypal Analysis for neuronal clique detection in low-rate calcium fluorescence imaging

Archetypal analysis (AA) is a versatile data analysis method to cluster distinct features within a data set. Here, we demonstrate a framework showing the power of AA to spatio-temporally resolve events in calcium imaging, an imaging modality commonly used in neurobiology and neuroscience to capture neuronal communication patterns. After validation of our AA-based approach on synthetic data sets, we were able to characterize neuronal communication patterns in recorded calcium waves. Clinical relevance- Transient calcium events play an essential role in brain cell communication, growth, and network formation, as well as in neurodegeneration. To reliably interpret calcium events from personalized medicine data, where patterns may differ from patient to patient, appropriate image processing and signal analysis methods need to be developed for optimal network characterization.

Self-organization of in vitro neuronal assemblies drives to complex network topology

Activity-dependent self-organization plays an important role in the formation of specific and stereotyped connectivity patterns in neural circuits. By combining neuronal cultures, and tools with approaches from network neuroscience and information theory, we can study how complex network topology emerges from local neuronal interactions. We constructed effective connectivity networks using a transfer entropy analysis of spike trains recorded from rat embryo dissociated hippocampal neuron cultures between 6 and 35 days in vitro to investigate how the topology evolves during maturation. The methodology for constructing the networks considered the synapse delay and addressed the influence of firing rate and population bursts as well as spurious effects on the inference of connections. We found that the number of links in the networks grew over the course of development, shifting from a segregated to a more integrated architecture. As part of this progression, three significant aspects of complex network topology emerged. In agreement with previous in silico and in vitro studies, a small-world architecture was detected, largely due to strong clustering among neurons. Additionally, the networks developed in a modular topology, with most modules comprising nearby neurons. Finally, highly active neurons acquired topological characteristics that made them important nodes to the network and integrators of modules. These findings leverage new insights into how neuronal effective network topology relates to neuronal assembly self-organization mechanisms.

Involvement of Mechanical Cues in the Migration of Cajal-Retzius Cells in the Marginal Zone During Neocortical Development

Emerging evidence points to coordinated action of chemical and mechanical cues during brain development. At early stages of neocortical development, angiogenic factors and chemokines such as CXCL12, ephrins, and semaphorins assume crucial roles in orchestrating neuronal migration and axon elongation of postmitotic neurons. Here we explore the intrinsic mechanical properties of the developing marginal zone of the pallium in the migratory pathways and brain distribution of the pioneer Cajal-Retzius cells. These neurons are generated in several proliferative regions in the developing brain (e.g., the cortical hem and the pallial subpallial boundary) and migrate tangentially in the preplate/marginal zone covering the upper portion of the developing cortex. These cells play crucial roles in correct neocortical layer formation by secreting several molecules such as Reelin. Our results indicate that the motogenic properties of Cajal-Retzius cells and their perinatal distribution in the marginal zone are modulated by both chemical and mechanical factors, by the specific mechanical properties of Cajal-Retzius cells, and by the differential stiffness of the migratory routes. Indeed, cells originating in the cortical hem display higher migratory capacities than those generated in the pallial subpallial boundary which may be involved in the differential distribution of these cells in the dorsal-lateral axis in the developing marginal zone.

Early lock-in of structured and specialised information flows during neural development

The brains of many organisms are capable of complicated distributed computation underpinned by a highly advanced information processing capacity. Although substantial progress has been made towards characterising the information flow component of this capacity in mature brains, there is a distinct lack of work characterising its emergence during neural development. This lack of progress has been largely driven by the lack of effective estimators of information processing operations for spiking data. Here, we leverage recent advances in this estimation task in order to quantify the changes in transfer entropy during development. We do so by studying the changes in the intrinsic dynamics of the spontaneous activity of developing dissociated neural cell cultures. We find that the quantity of information flowing across these networks undergoes a dramatic increase across development. Moreover, the spatial structure of these flows exhibits a tendency to lock-in at the point when they arise. We also characterise the flow of information during the crucial periods of population bursts. We find that, during these bursts, nodes tend to undertake specialised computational roles as either transmitters, mediators, or receivers of information, with these roles tending to align with their average spike ordering. Further, we find that these roles are regularly locked-in when the information flows are established. Finally, we compare these results to information flows in a model network developing according to a spike-timing-dependent plasticity learning rule. Similar temporal patterns in the development of information flows were observed in these networks, hinting at the broader generality of these phenomena.

Functional Implications of Dale's Law in Balanced Neuronal Network Dynamics and Decision Making

The notion that a neuron transmits the same set of neurotransmitters at all of its post-synaptic connections, typically known as Dale's law, is well supported throughout the majority of the brain and is assumed in almost all theoretical studies investigating the mechanisms for computation in neuronal networks. Dale's law has numerous functional implications in fundamental sensory processing and decision-making tasks, and it plays a key role in the current understanding of the structure-function relationship in the brain. However, since exceptions to Dale's law have been discovered for certain neurons and because other biological systems with complex network structure incorporate individual units that send both positive and negative feedback signals, we investigate the functional implications of network model dynamics that violate Dale's law by allowing each neuron to send out both excitatory and inhibitory signals to its neighbors. We show how balanced network dynamics, in which large excitatory and inhibitory inputs are dynamically adjusted such that input fluctuations produce irregular firing events, are theoretically preserved for a single population of neurons violating Dale's law. We further leverage this single-population network model in the context of two competing pools of neurons to demonstrate that effective decision-making dynamics are also produced, agreeing with experimental observations from honeybee dynamics in selecting a food source and artificial neural networks trained in optimal selection. Through direct comparison with the classical two-population balanced neuronal network, we argue that the one-population network demonstrates more robust balanced activity for systems with less computational units, such as honeybee colonies, whereas the two-population network exhibits a more rapid response to temporal variations in network inputs, as required by the brain. We expect this study will shed light on the role of neurons violating Dale's law found in experiment as well as shared design principles across biological systems that perform complex computations.

Analysis of co-isogenic prion protein deficient mice reveals behavioral deficits, learning impairment, and enhanced hippocampal excitability

Background

Cellular prion protein (PrP^C) is a cell surface GPI-anchored protein, usually known for its role in the pathogenesis of human and animal prionopathies. However, increasing knowledge about the participation of PrP^C in prion pathogenesis contrasts with puzzling data regarding its natural physiological role. PrP^C is expressed in a number of tissues, including at high levels in the nervous system, especially in neurons and glial cells, and while previous studies have established a neuroprotective role, conflicting evidence for a synaptic function has revealed both reduced and enhanced long-term potentiation, and variable observations on memory, learning, and behavior. Such evidence has been confounded by the absence of an appropriate knock-out mouse model to dissect the biological relevance of PrP^C, with some functions recently shown to be misattributed to PrP^C due to the presence of genetic artifacts in mouse models. Here we elucidate the role of PrP^C in the hippocampal circuitry and its related functions, such as learning and memory, using a recently available strictly co-isogenic Prnp^0/0 mouse model (Prnp^ZH3/ZH3).

Results

We performed behavioral and operant conditioning tests to evaluate memory and learning capabilities, with results showing decreased motility, impaired operant conditioning learning, and anxiety-related behavior in Prnp^ZH3/ZH3 animals. We also carried in vivo electrophysiological recordings on CA3-CA1 synapses in living behaving mice and monitored spontaneous neuronal firing and network formation in primary neuronal cultures of Prnp^ZH3/ZH3 vs wildtype mice. PrP^C absence enhanced susceptibility to high-intensity stimulations and kainate-induced seizures. However, long-term potentiation (LTP) was not enhanced in the Prnp^ZH3/ZH3 hippocampus. In addition, we observed a delay in neuronal maturation and network formation in Prnp^ZH3/ZH3 cultures.

Conclusion

Our results demonstrate that PrP^C promotes neuronal network formation and connectivity. PrP^C mediates synaptic function and protects the synapse from excitotoxic insults. Its deletion may underlie an epileptogenic-susceptible brain that fails to perform highly cognitive-demanding tasks such as associative learning and anxiety-like behaviors.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12915-021-01203-0.

Disparate insults relevant to schizophrenia converge on impaired spike synchrony and weaker synaptic interactions in prefrontal local circuits

Schizophrenia results from hundreds of known causes, including genetic, environmental, and developmental insults that cooperatively increase risk of developing the disease. In spite of the diversity of causal factors, schizophrenia presents with a core set of symptoms and brain abnormalities (both structural and functional) that particularly impact the prefrontal cortex. This suggests that many different causal factors leading to schizophrenia may cause prefrontal neurons and circuits to fail in fundamentally similar ways. The nature of convergent malfunctions in prefrontal circuits at the cell and synaptic levels leading to schizophrenia are not known. Here, we apply convergence-guided search to identify core pathological changes in the functional properties of prefrontal circuits that lie downstream of mechanistically distinct insults relevant to the disease. We compare the impacts of blocking NMDA receptors in monkeys and deleting a schizophrenia risk gene in mice on activity timing and effective communication in prefrontal local circuits. Although these manipulations operate through distinct molecular pathways and biological mechanisms, we found they produced convergent pathophysiological effects on prefrontal local circuits. Both manipulations reduced the frequency of synchronous (0-lag) spiking between prefrontal neurons and weakened functional interactions between prefrontal neurons at monosynaptic lags as measured by information transfer between the neurons. The two observations may be related, as reduction in synchronous spiking between prefrontal neurons would be expected to weaken synaptic connections between them via spike-timing-dependent synaptic plasticity. These data suggest that the link between spike timing and synaptic connectivity could comprise the functional vulnerability that multiple risk factors exploit to produce disease.

FARCI: Fast and Robust Connectome Inference

The inference of neuronal connectome from large-scale neuronal activity recordings, such as two-photon Calcium imaging, represents an active area of research in computational neuroscience. In this work, we developed FARCI (Fast and Robust Connectome Inference), a MATLAB package for neuronal connectome inference from high-dimensional two-photon Calcium fluorescence data. We employed partial correlations as a measure of the functional association strength between pairs of neurons to reconstruct a neuronal connectome. We demonstrated using in silico datasets from the Neural Connectomics Challenge (NCC) and those generated using the state-of-the-art simulator of Neural Anatomy and Optimal Microscopy (NAOMi) that FARCI provides an accurate connectome and its performance is robust to network sizes, missing neurons, and noise levels. Moreover, FARCI is computationally efficient and highly scalable to large networks. In comparison with the best performing connectome inference algorithm in the NCC, Generalized Transfer Entropy (GTE), and Fluorescence Single Neuron and Network Analysis Package (FluoroSNNAP), FARCI produces more accurate networks over different network sizes, while providing significantly better computational speed and scaling.

Information flow in the rat thalamo-cortical system: spontaneous vs. stimulus-evoked activities

The interaction between the thalamus and sensory cortex plays critical roles in sensory processing. Previous studies have revealed pathway-specific synaptic properties of thalamo-cortical connections. However, few studies to date have investigated how each pathway routes moment-to-moment information. Here, we simultaneously recorded neural activity in the auditory thalamus (or ventral division of the medial geniculate body; MGv) and primary auditory cortex (A1) with a laminar resolution in anesthetized rats. Transfer entropy (TE) was used as an information theoretic measure to operationalize “information flow”. Our analyses confirmed that communication between the thalamus and cortex was strengthened during presentation of auditory stimuli. In the resting state, thalamo-cortical communications almost disappeared, whereas intracortical communications were strengthened. The predominant source of information was the MGv at the onset of stimulus presentation and layer 5 during spontaneous activity. In turn, MGv was the major recipient of information from layer 6. TE suggested that a small but significant population of MGv-to-A1 pairs was “information-bearing,” whereas A1-to-MGv pairs typically exhibiting small effects played modulatory roles. These results highlight the capability of TE analyses to unlock novel avenues for bridging the gap between well-established anatomical knowledge of canonical microcircuits and physiological correlates via the concept of dynamic information flow.

Inferring Excitatory and Inhibitory Connections in Neuronal Networks

The comprehension of neuronal network functioning, from most basic mechanisms of signal transmission to complex patterns of memory and decision making, is at the basis of the modern research in experimental and computational neurophysiology. While mechanistic knowledge of neurons and synapses structure increased, the study of functional and effective networks is more complex, involving emergent phenomena, nonlinear responses, collective waves, correlation and causal interactions. Refined data analysis may help in inferring functional/effective interactions and connectivity from neuronal activity. The Transfer Entropy (TE) technique is, among other things, well suited to predict structural interactions between neurons, and to infer both effective and structural connectivity in small- and large-scale networks. To efficiently disentangle the excitatory and inhibitory neural activities, in the article we present a revised version of TE, split in two contributions and characterized by a suited delay time. The method is tested on in silico small neuronal networks, built to simulate the calcium activity as measured via calcium imaging in two-dimensional neuronal cultures. The inhibitory connections are well characterized, still preserving a high accuracy for excitatory connections prediction. The method could be applied to study effective and structural interactions in systems of excitable cells, both in physiological and in pathological conditions.

Super-Selective Reconstruction of Causal and Direct Connectivity With Application to in vitro iPSC Neuronal Networks

Despite advancements in the development of cell-based in-vitro neuronal network models, the lack of appropriate computational tools limits their analyses. Methods aimed at deciphering the effective connections between neurons from extracellular spike recordings would increase utility of in vitro local neural circuits, especially for studies of human neural development and disease based on induced pluripotent stem cells (hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fundamentally unable to correctly identify indirect and apparent connections between neurons, generating redundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe a novel mathematically rigorous, model-free method to map effective-direct and causal-connectivity of neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical and deterministic indicators which, first, enables identification of all existing functional links in the network and then reconstructs the directed and causal connection diagram via a super-selective rule enabling highly accurate classification of direct, indirect, and apparent links. Our method can be generally applied to the functional characterization of any in vitro neuronal networks. Here, we show that, given its accuracy, it can offer important insights into the functional development of in vitro hiPSC-derived neuronal cultures.

Inferring network properties from time series using transfer entropy and mutual information: Validation of multivariate versus bivariate approaches

Functional and effective networks inferred from time series are at the core of network neuroscience. Interpreting properties of these networks requires inferred network models to reflect key underlying structural features. However, even a few spurious links can severely distort network measures, posing a challenge for functional connectomes. We study the extent to which micro- and macroscopic properties of underlying networks can be inferred by algorithms based on mutual information and bivariate/multivariate transfer entropy. The validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Simulations are based on a neural mass model and on autoregressive dynamics (employing Gaussian estimators for direct comparison to functional connectivity and Granger causality). We find that multivariate transfer entropy captures key properties of all network structures for longer time series. Bivariate methods can achieve higher recall (sensitivity) for shorter time series but are unable to control false positives (lower specificity) as available data increases. This leads to overestimated clustering, small-world, and rich-club coefficients, underestimated shortest path lengths and hub centrality, and fattened degree distribution tails. Caution should therefore be used when interpreting network properties of functional connectomes obtained via correlation or pairwise statistical dependence measures, rather than more holistic (yet data-hungry) multivariate models.

We compare bivariate and multivariate methods for inferring networks from time series, which are generated using a neural mass model and autoregressive dynamics. We assess their ability to reproduce key properties of the underlying structural network. Validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Even a few spurious links can severely bias key network properties. Multivariate transfer entropy performs best on all topologies for longer time series.

Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data

Transfer entropy (TE) is a widely used measure of directed information flows in a number of domains including neuroscience. Many real-world time series for which we are interested in information flows come in the form of (near) instantaneous events occurring over time. Examples include the spiking of biological neurons, trades on stock markets and posts to social media, amongst myriad other systems involving events in continuous time throughout the natural and social sciences. However, there exist severe limitations to the current approach to TE estimation on such event-based data via discretising the time series into time bins: it is not consistent, has high bias, converges slowly and cannot simultaneously capture relationships that occur with very fine time precision as well as those that occur over long time intervals. Building on recent work which derived a theoretical framework for TE in continuous time, we present an estimation framework for TE on event-based data and develop a k-nearest-neighbours estimator within this framework. This estimator is provably consistent, has favourable bias properties and converges orders of magnitude more quickly than the current state-of-the-art in discrete-time estimation on synthetic examples. We demonstrate failures of the traditionally-used source-time-shift method for null surrogate generation. In order to overcome these failures, we develop a local permutation scheme for generating surrogate time series conforming to the appropriate null hypothesis in order to test for the statistical significance of the TE and, as such, test for the conditional independence between the history of one point process and the updates of another. Our approach is shown to be capable of correctly rejecting or accepting the null hypothesis of conditional independence even in the presence of strong pairwise time-directed correlations. This capacity to accurately test for conditional independence is further demonstrated on models of a spiking neural circuit inspired by the pyloric circuit of the crustacean stomatogastric ganglion, succeeding where previous related estimators have failed.

In Vitro Development of Human iPSC-Derived Functional Neuronal Networks on Laser-Fabricated 3D Scaffolds

Neural progenitor cells generated from human induced pluripotent stem cells (hiPSCs) are the forefront of ″brain-on-chip″ investigations. Viable and functional hiPSC-derived neuronal networks are shaping powerful in vitro models for evaluating the normal and abnormal formation of cortical circuits, understanding the underlying disease mechanisms, and investigating the response to drugs. They therefore represent a desirable instrument for both the scientific community and the pharmacological industry. However, culture conditions required for the full functional maturation of individual neurons and networks are still unidentified. It has been recognized that three-dimensional (3D) culture conditions can better emulate in vivo neuronal tissue development compared to 2D cultures and thus provide a more desirable in vitro approach. In this paper, we present the design and implementation of a 3D scaffold platform that supports and promotes intricate neuronal network development. 3D scaffolds were produced through direct laser writing by two-photon polymerization (2PP), a high-resolution 3D laser microstructuring technology, using the biocompatible and nondegradable photoreactive resin Dental LT Clear (DClear). Neurons developed and interconnected on a 3D environment shaped by vertically stacked scaffold layers. The developed networks could support different cell types. Starting at the day 50 of 3D culture, neuronal progenitor cells could develop into cortical projection neurons (CNPs) of all six layers, different types of inhibitory neurons, and glia. Additionally and in contrast to 2D conditions, 3D scaffolds supported the long-term culturing of neuronal networks over the course of 120 days. Network health and functionality were probed through calcium imaging, which revealed a strong spontaneous neuronal activity that combined individual and collective events. Taken together, our results highlight advanced microstructured 3D scaffolds as a reliable platform for the 3D in vitro modeling of neuronal functions.

TENET: gene network reconstruction using transfer entropy reveals key regulatory factors from single cell transcriptomic data

Accurate prediction of gene regulatory rules is important towards understanding of cellular processes. Existing computational algorithms devised for bulk transcriptomics typically require a large number of time points to infer gene regulatory networks (GRNs), are applicable for a small number of genes and fail to detect potential causal relationships effectively. Here, we propose a novel approach 'TENET' to reconstruct GRNs from single cell RNA sequencing (scRNAseq) datasets. Employing transfer entropy (TE) to measure the amount of causal relationships between genes, TENET predicts large-scale gene regulatory cascades/relationships from scRNAseq data. TENET showed better performance than other GRN reconstructors, in identifying key regulators from public datasets. Specifically from scRNAseq, TENET identified key transcriptional factors in embryonic stem cells (ESCs) and during direct cardiomyocytes reprogramming, where other predictors failed. We further demonstrate that known target genes have significantly higher TE values, and TENET predicted higher TE genes were more influenced by the perturbation of their regulator. Using TENET, we identified and validated that Nme2 is a culture condition specific stem cell factor. These results indicate that TENET is uniquely capable of identifying key regulators from scRNAseq data.

Functional strengthening through synaptic scaling upon connectivity disruption in neuronal cultures

An elusive phenomenon in network neuroscience is the extent of neuronal activity remodeling upon damage. Here, we investigate the action of gradual synaptic blockade on the effective connectivity in cortical networks in vitro. We use two neuronal cultures configurations-one formed by about 130 neuronal aggregates and another one formed by about 600 individual neurons-and monitor their spontaneous activity upon progressive weakening of excitatory connectivity. We report that the effective connectivity in all cultures exhibits a first phase of transient strengthening followed by a second phase of steady deterioration. We quantify these phases by measuring GEFF, the global efficiency in processing network information. We term hyperefficiency the sudden strengthening of GEFF upon network deterioration, which increases by 20-50% depending on culture type. Relying on numerical simulations we reveal the role of synaptic scaling, an activity-dependent mechanism for synaptic plasticity, in counteracting the perturbative action, neatly reproducing the observed hyperefficiency. Our results demonstrate the importance of synaptic scaling as resilience mechanism.

Impact of Physical Obstacles on the Structural and Effective Connectivity of in silico Neuronal Circuits

Scaffolds and patterned substrates are among the most successful strategies to dictate the connectivity between neurons in culture. Here, we used numerical simulations to investigate the capacity of physical obstacles placed on a flat substrate to shape structural connectivity, and in turn collective dynamics and effective connectivity, in biologically-realistic neuronal networks. We considered μ-sized obstacles placed in mm-sized networks. Three main obstacle shapes were explored, namely crosses, circles and triangles of isosceles profile. They occupied either a small area fraction of the substrate or populated it entirely in a periodic manner. From the point of view of structure, all obstacles promoted short length-scale connections, shifted the in- and out-degree distributions toward lower values, and increased the modularity of the networks. The capacity of obstacles to shape distinct structural traits depended on their density and the ratio between axonal length and substrate diameter. For high densities, different features were triggered depending on obstacle shape, with crosses trapping axons in their vicinity and triangles funneling axons along the reverse direction of their tip. From the point of view of dynamics, obstacles reduced the capacity of networks to spontaneously activate, with triangles in turn strongly dictating the direction of activity propagation. Effective connectivity networks, inferred using transfer entropy, exhibited distinct modular traits, indicating that the presence of obstacles facilitated the formation of local effective microcircuits. Our study illustrates the potential of physical constraints to shape structural blueprints and remodel collective activity, and may guide investigations aimed at mimicking organizational traits of biological neuronal circuits.

Inferring neural information flow from spiking data

The brain can be regarded as an information processing system in which neurons store and propagate information about external stimuli and internal processes. Therefore, estimating interactions between neural activity at the cellular scale has significant implications in understanding how neuronal circuits encode and communicate information across brain areas to generate behavior. While the number of simultaneously recorded neurons is growing exponentially, current methods relying only on pairwise statistical dependencies still suffer from a number of conceptual and technical challenges that preclude experimental breakthroughs describing neural information flows. In this review, we examine the evolution of the field over the years, starting from descriptive statistics to model-based and model-free approaches. Then, we discuss in detail the Granger Causality framework, which includes many popular state-of-the-art methods and we highlight some of its limitations from a conceptual and practical estimation perspective. Finally, we discuss directions for future research, including the development of theoretical information flow models and the use of dimensionality reduction techniques to extract relevant interactions from large-scale recording datasets.

Potential of Microfluidics and Lab-on-Chip Platforms to Improve Understanding of "prion-like" Protein Assembly and Behavior

Human aging is accompanied by a relevant increase in age-associated chronic pathologies, including neurodegenerative and metabolic diseases. The appearance and evolution of numerous neurodegenerative diseases is paralleled by the appearance of intracellular and extracellular accumulation of misfolded proteins in affected brains. In addition, recent evidence suggests that most of these amyloid proteins can behave and propagate among neural cells similarly to infective prions. In order to improve understanding of the seeding and spreading processes of these "prion-like" amyloids, microfluidics and 3D lab-on-chip approaches have been developed as highly valuable tools. These techniques allow us to monitor changes in cellular and molecular processes responsible for amyloid seeding and cell spreading and their parallel effects in neural physiology. Their compatibility with new optical and biochemical techniques and their relative availability have increased interest in them and in their use in numerous laboratories. In addition, recent advances in stem cell research in combination with microfluidic platforms have opened new humanized in vitro models for myriad neurodegenerative diseases affecting different cellular targets of the vascular, muscular, and nervous systems, and glial cells. These new platforms help reduce the use of animal experimentation. They are more reproducible and represent a potential alternative to classical approaches to understanding neurodegeneration. In this review, we summarize recent progress in neurobiological research in "prion-like" protein using microfluidic and 3D lab-on-chip approaches. These approaches are driven by various fields, including chemistry, biochemistry, and cell biology, and they serve to facilitate the development of more precise human brain models for basic mechanistic studies of cell-to-cell interactions and drug discovery.

Grafted human pluripotent stem cell-derived cortical neurons integrate into adult human cortical neural circuitry

Several neurodegenerative diseases cause loss of cortical neurons, leading to sensory, motor, and cognitive impairments. Studies in different animal models have raised the possibility that transplantation of human cortical neuronal progenitors, generated from pluripotent stem cells, might be developed into a novel therapeutic strategy for disorders affecting cerebral cortex. For example, we have shown that human long‐term neuroepithelial‐like stem (lt‐NES) cell‐derived cortical neurons, produced from induced pluripotent stem cells and transplanted into stroke‐injured adult rat cortex, improve neurological deficits and establish both afferent and efferent morphological and functional connections with host cortical neurons. So far, all studies with human pluripotent stem cell‐derived neurons have been carried out using xenotransplantation in animal models. Whether these neurons can integrate also into adult human brain circuitry is unknown. Here, we show that cortically fated lt‐NES cells, which are able to form functional synaptic networks in cell culture, differentiate to mature, layer‐specific cortical neurons when transplanted ex vivo onto organotypic cultures of adult human cortex. The grafted neurons are functional and establish both afferent and efferent synapses with adult human cortical neurons in the slices as evidenced by immuno‐electron microscopy, rabies virus retrograde monosynaptic tracing, and whole‐cell patch‐clamp recordings. Our findings provide the first evidence that pluripotent stem cell‐derived neurons can integrate into adult host neural networks also in a human‐to‐human grafting situation, thereby supporting their potential future clinical use to promote recovery by neuronal replacement in the patient's diseased brain.

Transfer Entropy as a Measure of Brain Connectivity: A Critical Analysis With the Help of Neural Mass Models

Objective: Assessing brain connectivity from electrophysiological signals is of great relevance in neuroscience, but results are still debated and depend crucially on how connectivity is defined and on mathematical instruments utilized. Aim of this work is to assess the capacity of bivariate Transfer Entropy (TE) to evaluate connectivity, using data generated from simple neural mass models of connected Regions of Interest (ROIs). Approach: Signals simulating mean field potentials were generated assuming two, three or four ROIs, connected via excitatory or by-synaptic inhibitory links. We investigated whether the presence of a statistically significant connection can be detected and if connection strength can be quantified. Main Results: Results suggest that TE can reliably estimate the strength of connectivity if neural populations work in their linear regions, and if the epoch lengths are longer than 10 s. In case of multivariate networks, some spurious connections can emerge (i.e., a statistically significant TE even in the absence of a true connection); however, quite a good correlation between TE and synaptic strength is still preserved. Moreover, TE appears more robust for distal regions (longer delays) compared with proximal regions (smaller delays): an approximate a priori knowledge on this delay can improve the procedure. Finally, non-linear phenomena affect the assessment of connectivity, since they may significantly reduce TE estimation: information transmission between two ROIs may be weak, due to non-linear phenomena, even if a strong causal connection is present. Significance: Changes in functional connectivity during different tasks or brain conditions, might not always reflect a true change in the connecting network, but rather a change in information transmission. A limitation of the work is the use of bivariate TE. In perspective, the use of multivariate TE can improve estimation and reduce some of the problems encountered in the present study.

Deficits in coordinated neuronal activity and network topology are striatal hallmarks in Huntington's disease

Background

Network alterations underlying neurodegenerative diseases often precede symptoms and functional deficits. Thus, their early identification is central for improved prognosis. In Huntington’s disease (HD), the cortico-striatal networks, involved in motor function processing, are the most compromised neural substrate. However, whether the network alterations are intrinsic of the striatum or the cortex is not fully understood.

Results

In order to identify early HD neural deficits, we characterized neuronal ensemble calcium activity and network topology of HD striatal and cortical cultures. We used large-scale calcium imaging combined with activity-based network inference analysis. We extracted collective activity events and inferred the topology of the neuronal network in cortical and striatal primary cultures from wild-type and R6/1 mouse model of HD. Striatal, but not cortical, HD networks displayed lower activity and a lessened ability to integrate information. GABA_A receptor blockade in healthy and HD striatal cultures generated similar coordinated ensemble activity and network topology, highlighting that the excitatory component of striatal system is spared in HD. Conversely, NMDA receptor activation increased individual neuronal activity while coordinated activity became highly variable and undefined. Interestingly, by boosting NMDA activity, we rectified striatal HD network alterations.

Conclusions

Overall, our integrative approach highlights striatal defective network integration capacity as a major contributor of basal ganglia dysfunction in HD and suggests that increased excitatory drive may serve as a potential intervention. In addition, our work provides a valuable tool to evaluate in vitro network recovery after treatment intervention in basal ganglia disorders.

Transfer Entropy in Artificial and Cardiovascular Environment in Stress

The paper examines the influence of acute and chronic stress on the relationship between systolic blood pressure (SBP) and pulse interval (PI) recorded from laboratory rats with different genetic predispositions for the development of the hypertensive disease. Transfer entropy (TE) was used to examine the direction of information flow between SBP and PI, spontaneous baroreflex sensitivity (BRS) was used to evaluate the ability of adaptation of PI time series to changes in SBP, and the cross-approximate entropy (XApEn) to quantify the SBP-PI synchronization. The effects of the time series length on TE estimation was also investigated in an artificial environment for the time series without a strong causal relation. The consistency of the TE estimation was achieved only for extremely long time series. The results showed that chronic stress influence on the increase in information transmission between SBP and PI (TE) while changes of (BRS) and XApEn were not noticed.

Reconstructing positive and negative couplings in Ising spin networks by sorted local transfer entropy

We employ the sorted local transfer entropy (SLTE) to reconstruct the coupling strengths of Ising spin networks with positive and negative couplings (J_{ij}), using only the time-series data of the spins. The SLTE method is model-free in the sense that no knowledge of the underlying dynamics of the spin system is required and is applicable to a broad class of systems. Contrary to the inference of coupling from pairwise transfer entropy, our method can reliably distinguish spin pair interactions with positive and negative couplings. The method is tested for the inverse Ising problem for different J_{ij} distributions and various spin dynamics, including synchronous and asynchronous update Glauber dynamics and Kawasaki exchange dynamics. It is found that the pairwise SLTE is proportional to the pairwise coupling strength to a good extent for all cases studied. In addition, the reconstruction works well for both the equilibrium and nonequilibrium cases of the time-series data. Comparison to other inverse Ising problem approaches using mean-field equations is also discussed.

Reconstruction of Functional Connectivity from Multielectrode Recordings and Calcium Imaging

In the last two decades, increasing research efforts in neuroscience have been focused on determining both structural and functional connectivity of brain circuits, with the main goal of relating the wiring diagram of neuronal systems to their emerging properties, from the microscale to the macroscale. While combining multisite parallel recordings with structural circuits' reconstruction in vivo is still very challenging, the reductionist in vitro approach based on neuronal cultures offers lower technical difficulties and is much more stable under control conditions. In this chapter, we present different approaches to infer the connectivity of cultured neuronal networks using multielectrode array or calcium imaging recordings. We first formally introduce the used methods, and then we will describe into details how those methods were applied in case studies. Since multielectrode array and calcium imaging recordings provide distinct and complementary spatiotemporal features of neuronal activity, in this chapter we present the strategies implemented with the two different methodologies in distinct sections.

Inferring information flow in spike-train data sets using a trial-shuffle method

Understanding information processing in the brain requires the ability to determine the functional connectivity between the different regions of the brain. We present a method using transfer entropy to extract this flow of information between brain regions from spike-train data commonly obtained in neurological experiments. Transfer entropy is a statistical measure based in information theory that attempts to quantify the information flow from one process to another, and has been applied to find connectivity in simulated spike-train data. Due to statistical error in the estimator, inferring functional connectivity requires a method for determining significance in the transfer entropy values. We discuss the issues with numerical estimation of transfer entropy and resulting challenges in determining significance before presenting the trial-shuffle method as a viable option. The trial-shuffle method, for spike-train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons by comparing to a created baseline distribution using a rigorous statistical test. This is in contrast to either globally comparing all neuron transfer entropy values or comparing pairwise values to a single baseline value. In establishing the viability of this method by comparison to several alternative approaches in the literature, we find evidence that preserving the inter-spike-interval timing is important. We then use the trial-shuffle method to investigate information flow within a model network as we vary model parameters. This includes investigating the global flow of information within a connectivity network divided into two well-connected subnetworks, going beyond local transfer of information between pairs of neurons.

Assessing functional connectivity across 3D tissue engineered axonal tracts using calcium fluorescence imaging

OBJECTIVE

Micro-tissue engineered neural networks (micro-TENNs) are anatomically-inspired constructs designed to structurally and functionally emulate white matter pathways in the brain. These 3D neural networks feature long axonal tracts spanning discrete neuronal populations contained within a tubular hydrogel, and are being developed to reconstruct damaged axonal pathways in the brain as well as to serve as physiologically-relevant in vitro experimental platforms. The goal of the current study was to characterize the functional properties of these neuronal and axonal networks.

APPROACH

Bidirectional micro-TENNs were transduced to express genetically-encoded calcium indicators, and spontaneous fluorescence activity was recorded using real-time microscopy at 20 Hz from specific regions-of-interest in the neuronal populations. Network activity patterns and functional connectivity across the axonal tracts were then assessed using various techniques from statistics and information theory including Pearson cross-correlation, phase synchronization matrices, power spectral analysis, directed transfer function, and transfer entropy.

MAIN RESULTS

Pearson cross-correlation, phase synchronization matrices, and power spectral analysis revealed high values of correlation and synchronicity between the spatially segregated neuronal clusters connected by axonal tracts. Specifically, phase synchronization revealed high synchronicity of  >0.8 between micro-TENN regions of interest. Normalized directed transfer function and transfer entropy matrices suggested robust information flow between the neuronal populations. Time varying power spectrum analysis revealed the strength of information propagation at various frequencies. Signal power strength was visible at elevated peak levels for dominant delta (1-4 Hz) and theta (4-8 Hz) frequency bands and progressively weakened at higher frequencies. These signal power strength results closely matched normalized directed transfer function analysis where near synchronous information flow was detected between frequencies of 2-5 Hz.

SIGNIFICANCE

To our knowledge, this is the first report using directed transfer function and transfer entropy methods based on fluorescent calcium activity to estimate functional connectivity of distinct neuronal populations via long-projecting, 3D axonal tracts in vitro. These functional data will further improve the design and optimization of implantable neural networks that could ultimately be deployed to reconstruct the nervous system to treat neurological disease and injury.

Entropy in Cell Biology: Information Thermodynamics of a Binary Code and Szilard Engine Chain Model of Signal Transduction

A model of signal transduction from the perspective of informational thermodynamics has been reported in recent studies, and several important achievements have been obtained. The first achievement is that signal transduction can be modelled as a binary code system, in which two forms of signalling molecules are utilised in individual steps. The second is that the average entropy production rate is consistent during the signal transduction cascade when the signal event number is maximised in the model. The third is that a Szilard engine can be a single-step model in the signal transduction. This article reviews these achievements and further introduces a new chain of Szilard engines as a biological reaction cascade (BRC) model. In conclusion, the presented model provides a way of computing the channel capacity of a BRC.

Transcranial Direct Current Stimulation (tDCS) Can Modulate EEG Complexity of Children With Autism Spectrum Disorder

Autism spectrum disorder (ASD) is a heterogeneous neurodevelopmental disorder which affects the developmental trajectory in several behavioral domains, including impairments of social communication, cognitive and language abilities. Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique, and it was used for modulating the brain disorders. In this paper, we enrolled 13 ASD children (11 males and 2 females; mean ± SD age: 6.5 ± 1.7 years) to participate in our trial. Each patient received 10 treatments over the dorsolateral prefrontal cortex (DLPFC) once every 2 days. Also, we enrolled 13 ASD children (11 males and 2 females; mean ± SD age: 6.3 ± 1.7 years) waiting to receive therapy as controls. A maximum entropy ratio (MER) method was adapted to measure the change of complexity of EEG series. It was found that the MER value significantly increased after tDCS. This study suggests that tDCS may be a helpful tool for the rehabilitation of children with ASD.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions.

Inferring structural connectivity using Ising couplings in models of neuronal networks

Functional connectivity metrics have been widely used to infer the underlying structural connectivity in neuronal networks. Maximum entropy based Ising models have been suggested to discount the effect of indirect interactions and give good results in inferring the true anatomical connections. However, no benchmarking is currently available to assess the performance of Ising couplings against other functional connectivity metrics in the microscopic scale of neuronal networks through a wide set of network conditions and network structures. In this paper, we study the performance of the Ising model couplings to infer the synaptic connectivity in in silico networks of neurons and compare its performance against partial and cross-correlations for different correlation levels, firing rates, network sizes, network densities, and topologies. Our results show that the relative performance amongst the three functional connectivity metrics depends primarily on the network correlation levels. Ising couplings detected the most structural links at very weak network correlation levels, and partial correlations outperformed Ising couplings and cross-correlations at strong correlation levels. The result was consistent across varying firing rates, network sizes, and topologies. The findings of this paper serve as a guide in choosing the right functional connectivity tool to reconstruct the structural connectivity.

Pre-processing and transfer entropy measures in motor neurons controlling limb movements

Directed information transfer measures are increasingly being employed in modeling neural system behavior due to their model-free approach, applicability to nonlinear and stochastic signals, and the potential to integrate repetitions of an experiment. Intracellular physiological recordings of graded synaptic potentials provide a number of additional challenges compared to spike signals due to non-stationary behaviour generated through extrinsic processes. We therefore propose a method to overcome this difficulty by using a preprocessing step based on Singular Spectrum Analysis (SSA) to remove nonlinear trends and discontinuities. We apply the method to intracellular recordings of synaptic responses of identified motor neurons evoked by stimulation of a proprioceptor that monitors limb position in leg of the desert locust. We then apply normalized delayed transfer entropy measures to neural responses evoked by displacements of the proprioceptor, the femoral chordotonal organ, that contains sensory neurones that monitor movements about the femoral-tibial joint. We then determine the consistency of responses within an individual recording of an identified motor neuron in a single animal, between repetitions of the same experiment in an identified motor neurons in the same animal and in repetitions of the same experiment from the same identified motor neuron in different animals. We found that delayed transfer entropy measures were consistent for a given identified neuron within and between animals and that they predict neural connectivity for the fast extensor tibiae motor neuron.

Effects of local network topology on the functional reconstruction of spiking neural network models

The representation of information flow through structural networks, as depicted by functional networks, does not coincide exactly with the anatomical configuration of the networks. Model free correlation methods including transfer entropy (TE) and a Gaussian convolution-based correlation method (CC) detect functional networks, i.e. temporal correlations in spiking activity among neurons, and depict information flow as a graph. The influence of synaptic topology on these functional correlations is not well-understood, though nonrandom features of the resulting functional structure (e.g. small-worldedness, motifs) are believed to play a crucial role in information-processing. We apply TE and CC to simulated networks with prescribed small-world and recurrence properties to obtain functional reconstructions which we compare with the underlying synaptic structure using multiplex networks. In particular, we examine the effects of the surrounding local synaptic circuitry on functional correlations by comparing dyadic and triadic subgraphs within the structural and functional graphs in order to explain recurring patterns of information flow on the level of individual neurons. Statistical significance is demonstrated by employing randomized null models and Z-scores, and results are obtained for functional networks reconstructed across a range of correlation-threshold values. From these results, we observe that certain triadic structural subgraphs have strong influence over functional topology.

Flexible information routing by transient synchrony

Perception, cognition and behavior rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying rapid information rerouting between such microcircuits are still unknown. It has been proposed that changing patterns of coherence between local gamma rhythms support flexible information rerouting. The stochastic and transient nature of gamma oscillations in vivo, however, is hard to reconcile with such a function. Here we show that models of cortical circuits near the onset of oscillatory synchrony selectively route input signals despite the short duration of gamma bursts and the irregularity of neuronal firing. In canonical multiarea circuits, we find that gamma bursts spontaneously arise with matched timing and frequency and that they organize information flow by large-scale routing states. Specific self-organized routing states can be induced by minor modulations of background activity.

Recurrence measure of conditional dependence and applications

Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Here we propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.

Understanding Policy Diffusion in the U.S.: An Information-Theoretical Approach to Unveil Connectivity Structures in Slowly Evolving Complex Systems

Detecting and explaining the relationships among interacting components has long been a focal point of dynamical systems research. In this paper, we extend these types of data-driven analyses to the realm of public policy, whereby individual legislative entities interact to produce changes in their legal and political environments. We focus on the U.S. public health policy landscape, whose complexity determines our capacity as a society to effectively tackle pressing health issues. It has long been thought that some U.S. states innovate and enact new policies, while others mimic successful or competing states. However, the extent to which states learn from others, and the state characteristics that lead two states to influence one another, are not fully understood. Here, we propose a model-free, information-theoretical method to measure the existence and direction of influence of one state's policy or legal activity on others. Specifically, we tailor a popular notion of causality to handle the slow time-scale of policy adoption dynamics and unravel relationships among states from their recent law enactment histories. The method is validated using surrogate data generated from a new stochastic model of policy activity. Through the analysis of real data in alcohol, driving safety, and impaired driving policy, we provide evidence for the role of geography, political ideology, risk factors, and demographic and economic indicators on a state's tendency to learn from others when shaping its approach to public health regulation. Our method offers a new model-free approach to uncover interactions and establish cause-and-effect in slowly-evolving complex dynamical systems.

Invisible Brain: Knowledge in Research Works and Neuron Activity

If the market has an invisible hand, does knowledge creation and representation have an "invisible brain"? While knowledge is viewed as a product of neuron activity in the brain, can we identify knowledge that is outside the brain but reflects the activity of neurons in the brain? This work suggests that the patterns of neuron activity in the brain can be seen in the representation of knowledge-related activity. Here we show that the neuron activity mechanism seems to represent much of the knowledge learned in the past decades based on published articles, in what can be viewed as an "invisible brain" or collective hidden neural networks. Similar results appear when analyzing knowledge activity in patents. Our work also tries to characterize knowledge increase as neuron network activity growth. The results propose that knowledge-related activity can be seen outside of the neuron activity mechanism. Consequently, knowledge might exist as an independent mechanism.

Rich-Club Organization in Effective Connectivity among Cortical Neurons

The performance of complex networks, like the brain, depends on how effectively their elements communicate. Despite the importance of communication, it is virtually unknown how information is transferred in local cortical networks, consisting of hundreds of closely spaced neurons. To address this, it is important to record simultaneously from hundreds of neurons at a spacing that matches typical axonal connection distances, and at a temporal resolution that matches synaptic delays. We used a 512-electrode array (60 μm spacing) to record spontaneous activity at 20 kHz from up to 500 neurons simultaneously in slice cultures of mouse somatosensory cortex for 1 h at a time. We applied a previously validated version of transfer entropy to quantify information transfer. Similar to in vivo reports, we found an approximately lognormal distribution of firing rates. Pairwise information transfer strengths also were nearly lognormally distributed, similar to reports of synaptic strengths. Some neurons transferred and received much more information than others, which is consistent with previous predictions. Neurons with the highest outgoing and incoming information transfer were more strongly connected to each other than chance, thus forming a "rich club." We found similar results in networks recorded in vivo from rodent cortex, suggesting the generality of these findings. A rich-club structure has been found previously in large-scale human brain networks and is thought to facilitate communication between cortical regions. The discovery of a small, but information-rich, subset of neurons within cortical regions suggests that this population will play a vital role in communication, learning, and memory. Significance statement: Many studies have focused on communication networks between cortical brain regions. In contrast, very few studies have examined communication networks within a cortical region. This is the first study to combine such a large number of neurons (several hundred at a time) with such high temporal resolution (so we can know the direction of communication between neurons) for mapping networks within cortex. We found that information was not transferred equally through all neurons. Instead, ∼70% of the information passed through only 20% of the neurons. Network models suggest that this highly concentrated pattern of information transfer would be both efficient and robust to damage. Therefore, this work may help in understanding how the cortex processes information and responds to neurodegenerative diseases.

Functional Clusters, Hubs, and Communities in the Cortical Microconnectome

Although relationships between networks of different scales have been observed in macroscopic brain studies, relationships between structures of different scales in networks of neurons are unknown. To address this, we recorded from up to 500 neurons simultaneously from slice cultures of rodent somatosensory cortex. We then measured directed effective networks with transfer entropy, previously validated in simulated cortical networks. These effective networks enabled us to evaluate distinctive nonrandom structures of connectivity at 2 different scales. We have 4 main findings. First, at the scale of 3-6 neurons (clusters), we found that high numbers of connections occurred significantly more often than expected by chance. Second, the distribution of the number of connections per neuron (degree distribution) had a long tail, indicating that the network contained distinctively high-degree neurons, or hubs. Third, at the scale of tens to hundreds of neurons, we typically found 2-3 significantly large communities. Finally, we demonstrated that communities were relatively more robust than clusters against shuffling of connections. We conclude the microconnectome of the cortex has specific organization at different scales, as revealed by differences in robustness. We suggest that this information will help us to understand how the microconnectome is robust against damage.

Activity and High-Order Effective Connectivity Alterations in Sanfilippo C Patient-Specific Neuronal Networks

Induced pluripotent stem cell (iPSC) technology has been successfully used to recapitulate phenotypic traits of several human diseases in vitro. Patient-specific iPSC-based disease models are also expected to reveal early functional phenotypes, although this remains to be proved. Here, we generated iPSC lines from two patients with Sanfilippo type C syndrome, a lysosomal storage disorder with inheritable progressive neurodegeneration. Mature neurons obtained from patient-specific iPSC lines recapitulated the main known phenotypes of the disease, not present in genetically corrected patient-specific iPSC-derived cultures. Moreover, neuronal networks organized in vitro from mature patient-derived neurons showed early defects in neuronal activity, network-wide degradation, and altered effective connectivity. Our findings establish the importance of iPSC-based technology to identify early functional phenotypes, which can in turn shed light on the pathological mechanisms occurring in Sanfilippo syndrome. This technology also has the potential to provide valuable readouts to screen compounds, which can prevent the onset of neurodegeneration.

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Fibroblasts from two Sanfilippo C patients were reprogrammed to obtain iPSCs

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iPSCs were successfully differentiated to neural cells that mimic the disease

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Networks of patients’ neurons show altered activity and connectivity

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Early functional phenotypes are prevented in gene-corrected patients’ neurons

Automated quantification of neuronal networks and single-cell calcium dynamics using calcium imaging

BACKGROUND

Recent advances in genetically engineered calcium and membrane potential indicators provide the potential to estimate the activation dynamics of individual neurons within larger, mesoscale networks (100s-1000+neurons). However, a fully integrated automated workflow for the analysis and visualization of neural microcircuits from high speed fluorescence imaging data is lacking.

NEW METHOD

Here we introduce FluoroSNNAP, Fluorescence Single Neuron and Network Analysis Package. FluoroSNNAP is an open-source, interactive software developed in MATLAB for automated quantification of numerous biologically relevant features of both the calcium dynamics of single-cells and network activity patterns. FluoroSNNAP integrates and improves upon existing tools for spike detection, synchronization analysis, and inference of functional connectivity, making it most useful to experimentalists with little or no programming knowledge.

RESULTS

We apply FluoroSNNAP to characterize the activity patterns of neuronal microcircuits undergoing developmental maturation in vitro. Separately, we highlight the utility of single-cell analysis for phenotyping a mixed population of neurons expressing a human mutant variant of the microtubule associated protein tau and wild-type tau.

COMPARISON WITH EXISTING METHOD(S)

We show the performance of semi-automated cell segmentation using spatiotemporal independent component analysis and significant improvement in detecting calcium transients using a template-based algorithm in comparison to peak-based or wavelet-based detection methods. Our software further enables automated analysis of microcircuits, which is an improvement over existing methods.

CONCLUSIONS

We expect the dissemination of this software will facilitate a comprehensive analysis of neuronal networks, promoting the rapid interrogation of circuits in health and disease.