Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals

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.

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

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.

Preparation and Mechano-Functional Characterization of PEGylated Fibrin Hydrogels: Impact of Thrombin Concentration

Three-dimensional (3D) neuronal cultures grown in hydrogels are promising platforms to design brain-like neuronal networks in vitro. However, the optimal properties of such cultures must be tuned to ensure a hydrogel matrix sufficiently porous to promote healthy development but also sufficiently rigid for structural support. Such an optimization is difficult since it implies the exploration of different hydrogel compositions and, at the same time, a functional analysis to validate neuronal culture viability. To advance in this quest, here we present a combination of a rheological protocol and a network-based functional analysis to investigate PEGylated fibrin hydrogel networks with gradually higher stiffness, achieved by increasing the concentration of thrombin. We observed that moderate thrombin concentrations of 10% and 25% in volume shaped healthy networks, although the functional traits depended on the hydrogel stiffness, which was much higher for the latter concentration. Thrombin concentrations of 65% or higher led to networks that did not survive. Our results illustrate the difficulties and limitations in preparing 3D neuronal networks, and stress the importance of combining a mechano-structural characterization of a biomaterial with a functional one.

Neuropathic pain following spinal cord hemisection induced by the reorganization in primary somatosensory cortex and regulated by neuronal activity of lateral parabrachial nucleus

AIMS

Neuropathic pain after spinal cord injury (SCI) remains a common and thorny problem, influencing the life quality severely. This study aimed to elucidate the reorganization of the primary sensory cortex (S1) and the regulatory mechanism of the lateral parabrachial nucleus (lPBN) in the presence of allodynia or hyperalgesia after left spinal cord hemisection injury (LHS).

METHODS

Through behavioral tests, we first identified mechanical allodynia and thermal hyperalgesia following LHS. We then applied two-photon microscopy to observe calcium activity in S1 during mechanical or thermal stimulation and long-term spontaneous calcium activity after LHS. By slice patch clamp recording, the electrophysiological characteristics of neurons in lPBN were explored. Finally, exploiting chemogenetic activation or inhibition of the neurons in lPBN, allodynia or hyperalgesia was regulated.

RESULTS

The calcium activity in left S1 was increased during mechanical stimulation of right hind limb and thermal stimulation of tail, whereas in right S1 it was increased only with thermal stimulation of tail. The spontaneous calcium activity in right S1 changed more dramatically than that in left S1 after LHS. The lPBN was also activated after LHS, and exploiting chemogenetic activation or inhibition of the neurons in lPBN could induce or alleviate allodynia and hyperalgesia in central neuropathic pain.

CONCLUSION

The neuronal activity changes in S1 are closely related to limb pain, which has accurate anatomical correspondence. After LHS, the spontaneously increased functional connectivity of calcium transient in left S1 is likely causing the mechanical allodynia in right hind limb and increased neuronal activity in bilateral S1 may induce thermal hyperalgesia in tail. This state of allodynia and hyperalgesia can be regulated by lPBN.

Mutual generation in neuronal activity across the brain via deep neural approach, and its network interpretation

In the brain, many regions work in a network-like association, yet it is not known how durable these associations are in terms of activity and could survive without structural connections. To assess the association or similarity between brain regions with a generating approach, this study evaluated the similarity of activities of neurons within each region after disconnecting between regions. The "generation" approach here refers to using a multi-layer LSTM (Long Short-Term Memory) model to learn the rules of activity generation in one region and then apply that knowledge to generate activity in other regions. Surprisingly, the results revealed that activity generation from one region to disconnected regions was possible with similar accuracy to generation between the same regions in many cases. Notably, firing rates and synchronization of firing between neuron pairs, often used as neuronal representations, could be reproduced with precision. Additionally, accuracies were associated with the relative angle between brain regions and the strength of the structural connections that initially connected them. This outcome enables us to look into trends governing non-uniformity of the cortex based on the potential to generate informative data and reduces the need for animal experiments.

Whole-Brain Evaluation of Cortical Microconnectomes

The brain is an organ that functions as a network of many elements connected in a nonuniform manner. In the brain, the neocortex is evolutionarily newest and is thought to be primarily responsible for the high intelligence of mammals. In the mature mammalian brain, all cortical regions are expected to have some degree of homology, but have some variations of local circuits to achieve specific functions performed by individual regions. However, few cellular-level studies have examined how the networks within different cortical regions differ. This study aimed to find rules for systematic changes of connectivity (microconnectomes) across 16 different cortical region groups. We also observed unknown trends in basic parameters in vitro such as firing rate and layer thickness across brain regions. Results revealed that the frontal group shows unique characteristics such as dense active neurons, thick cortex, and strong connections with deeper layers. This suggests the frontal side of the cortex is inherently capable of driving, even in isolation and that frontal nodes provide the driving force generating a global pattern of spontaneous synchronous activity, such as the default mode network. This finding provides a new hypothesis explaining why disruption in the frontal region causes a large impact on mental health.

Identifying properties of pattern completion neurons in a computational model of the visual cortex

Neural ensembles are found throughout the brain and are believed to underlie diverse cognitive functions including memory and perception. Methods to activate ensembles precisely, reliably, and quickly are needed to further study the ensembles' role in cognitive processes. Previous work has found that ensembles in layer 2/3 of the visual cortex (V1) exhibited pattern completion properties: ensembles containing tens of neurons were activated by stimulation of just two neurons. However, methods that identify pattern completion neurons are underdeveloped. In this study, we optimized the selection of pattern completion neurons in simulated ensembles. We developed a computational model that replicated the connectivity patterns and electrophysiological properties of layer 2/3 of mouse V1. We identified ensembles of excitatory model neurons using K-means clustering. We then stimulated pairs of neurons in identified ensembles while tracking the activity of the entire ensemble. Our analysis of ensemble activity quantified a neuron pair's power to activate an ensemble using a novel metric called pattern completion capability (PCC) based on the mean pre-stimulation voltage across the ensemble. We found that PCC was directly correlated with multiple graph theory parameters, such as degree and closeness centrality. To improve selection of pattern completion neurons in vivo, we computed a novel latency metric that was correlated with PCC and could potentially be estimated from modern physiological recordings. Lastly, we found that stimulation of five neurons could reliably activate ensembles. These findings can help researchers identify pattern completion neurons to stimulate in vivo during behavioral studies to control ensemble activation.

Astrocyte dysfunction and neuronal network hyperactivity in a CRISPR engineered pluripotent stem cell model of frontotemporal dementia

Frontotemporal dementia (FTD) is the second most prevalent type of early-onset dementia and up to 40% of cases are familial forms. One of the genes mutated in patients is CHMP2B, which encodes a protein found in a complex important for maturation of late endosomes, an essential process for recycling membrane proteins through the endolysosomal system. Here, we have generated a CHMP2B-mutated human embryonic stem cell line using genome editing with the purpose to create a human in vitro FTD disease model. To date, most studies have focused on neuronal alterations; however, we present a new co-culture system in which neurons and astrocytes are independently generated from human embryonic stem cells and combined in co-cultures. With this approach, we have identified alterations in the endolysosomal system of FTD astrocytes, a higher capacity of astrocytes to uptake and respond to glutamate, and a neuronal network hyperactivity as well as excessive synchronization. Overall, our data indicates that astrocyte alterations precede neuronal impairments and could potentially trigger neuronal network changes, indicating the important and specific role of astrocytes in disease development.

Impact of Magnetite Nanowires on In Vitro Hippocampal Neural Networks

Nanomaterials design, synthesis, and characterization are ever-expanding approaches toward developing biodevices or neural interfaces to treat neurological diseases. The ability of nanomaterials features to tune neuronal networks' morphology or functionality is still under study. In this work, we unveil how interfacing mammalian brain cultured neurons and iron oxide nanowires' (NWs) orientation affect neuronal and glial densities and network activity. Iron oxide NWs were synthesized by electrodeposition, fixing the diameter to 100 nm and the length to 1 µm. Scanning electron microscopy, Raman, and contact angle measurements were performed to characterize the NWs' morphology, chemical composition, and hydrophilicity. Hippocampal cultures were seeded on NWs devices, and after 14 days, the cell morphology was studied by immunocytochemistry and confocal microscopy. Live calcium imaging was performed to study neuronal activity. Using random nanowires (R-NWs), higher neuronal and glial cell densities were obtained compared with the control and vertical nanowires (V-NWs), while using V-NWs, more stellate glial cells were found. R-NWs produced a reduction in neuronal activity, while V-NWs increased the neuronal network activity, possibly due to a higher neuronal maturity and a lower number of GABAergic neurons, respectively. These results highlight the potential of NWs manipulations to design ad hoc regenerative interfaces.

Structural Modularity Tunes Mesoscale Criticality in Biological Neuronal Networks

Numerous studies suggest that biological neuronal networks self-organize toward a critical state with stable recruitment dynamics. Individual neurons would then statistically activate exactly one further neuron during activity cascades termed neuronal avalanches. Yet, it is unclear if and how this can be reconciled with the explosive recruitment dynamics within neocortical minicolumns in vivo and within neuronal clusters in vitro, which indicates that neurons form supercritical local circuits. Theoretical studies propose that modular networks with a mix of regionally subcritical and supercritical dynamics would create apparently critical dynamics, resolving this inconsistency. Here, we provide experimental support by manipulating the structural self-organization process of networks of cultured rat cortical neurons (either sex). Consistent with the prediction, we show that increasing clustering in neuronal networks developing in vitro strongly correlates with avalanche size distributions transitioning from supercritical to subcritical activity dynamics. Avalanche size distributions approximated a power law in moderately clustered networks, indicating overall critical recruitment. We propose that activity-dependent self-organization can tune inherently supercritical networks toward mesoscale criticality by creating a modular structure in neuronal networks.SIGNIFICANCE STATEMENT Critical recruitment dynamics in neuronal networks are considered optimal for information processing in the brain. However, it remains heavily debated how neuronal networks would self-organize criticality by detailed fine-tuning of connectivity, inhibition, and excitability. We provide experimental support for theoretical considerations that modularity tunes critical recruitment dynamics at the mesoscale level of interacting neuron clusters. This reconciles reports of supercritical recruitment dynamics in local neuron clusters with findings on criticality sampled at mesoscopic network scales. Intriguingly, altered mesoscale organization is a prominent aspect of various neuropathological diseases currently investigated in the framework of criticality. We therefore believe that our findings would also be of interest for clinical scientists searching to link the functional and anatomic signatures of such brain disorders.

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.

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks

Reconstructing the recurrent structural connectivity of neuronal networks is a challenge crucial to address in characterizing neuronal computations. While directly measuring the detailed connectivity structure is generally prohibitive for large networks, we develop a novel framework for reverse-engineering large-scale recurrent network connectivity matrices from neuronal dynamics by utilizing the widespread sparsity of neuronal connections. We derive a linear input-output mapping that underlies the irregular dynamics of a model network composed of both excitatory and inhibitory integrate-and-fire neurons with pulse coupling, thereby relating network inputs to evoked neuronal activity. Using this embedded mapping and experimentally feasible measurements of the firing rate as well as voltage dynamics in response to a relatively small ensemble of random input stimuli, we efficiently reconstruct the recurrent network connectivity via compressive sensing techniques. Through analogous analysis, we then recover high dimensional natural stimuli from evoked neuronal network dynamics over a short time horizon. This work provides a generalizable methodology for rapidly recovering sparse neuronal network data and underlines the natural role of sparsity in facilitating the efficient encoding of network data in neuronal dynamics.

Long-term calcium imaging reveals functional development in hiPSC-derived cultures comparable to human but not rat primary cultures

Models for human brain-oriented research are often established on primary cultures from rodents, which fails to recapitulate cellular specificity and molecular cues of the human brain. Here we investigated whether neuronal cultures derived from human induced pluripotent stem cells (hiPSCs) feature key advantages compared with rodent primary cultures. Using calcium fluorescence imaging, we tracked spontaneous neuronal activity in hiPSC-derived, human, and rat primary cultures and compared their dynamic and functional behavior as they matured. We observed that hiPSC-derived cultures progressively changed upon development, exhibiting gradually richer activity patterns and functional traits. By contrast, rat primary cultures were locked in the same dynamic state since activity onset. Human primary cultures exhibited features in between hiPSC-derived and rat primary cultures, although traits from the former predominated. Our study demonstrates that hiPSC-derived cultures are excellent models to investigate development in neuronal assemblies, a hallmark for applications that monitor alterations caused by damage or neurodegeneration.

Dynamic and Functional Alterations of Neuronal Networks In Vitro upon Physical Damage: A Proof of Concept

There is a growing technological interest in combining biological neuronal networks with electronic ones, specifically for biological computation, human-machine interfacing and robotic implants. A major challenge for the development of these technologies is the resilience of the biological networks to physical damage, for instance, when used in harsh environments. To tackle this question, here, we investigated the dynamic and functional alterations of rodent cortical networks grown in vitro that were physically damaged, either by sequentially removing groups of neurons that were central for information flow or by applying an incision that cut the network in half. In both cases, we observed a remarkable capacity of the neuronal cultures to cope with damage, maintaining their activity and even reestablishing lost communication pathways. We also observed-particularly for the cultures cut in half-that a reservoir of healthy neurons surrounding the damaged region could boost resilience by providing stimulation and a communication bridge across disconnected areas. Our results show the remarkable capacity of neuronal cultures to sustain and recover from damage, and may be inspirational for the development of future hybrid biological-electronic systems.

Rich dynamics and functional organization on topographically designed neuronal networks in vitro

Neuronal cultures are a prominent experimental tool to understand complex functional organization in neuronal assemblies. However, neurons grown on flat surfaces exhibit a strongly coherent bursting behavior with limited functionality. To approach the functional richness of naturally formed neuronal circuits, here we studied neuronal networks grown on polydimethylsiloxane (PDMS) topographical patterns shaped as either parallel tracks or square valleys. We followed the evolution of spontaneous activity in these cultures along 20 days in vitro using fluorescence calcium imaging. The networks were characterized by rich spatiotemporal activity patterns that comprised from small regions of the culture to its whole extent. Effective connectivity analysis revealed the emergence of spatially compact functional modules that were associated with both the underpinned topographical features and predominant spatiotemporal activity fronts. Our results show the capacity of spatial constraints to mold activity and functional organization, bringing new opportunities to comprehend the structure-function relationship in living neuronal circuits.

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.

Diverse operant control of different motor cortex populations during learning

During motor learning,1 as well as during neuroprosthetic learning,2-4 animals learn to control motor cortex activity in order to generate behavior. Two different populations of motor cortex neurons, intra-telencephalic (IT) and pyramidal tract (PT) neurons, convey the resulting cortical signals within and outside the telencephalon. Although a large amount of evidence demonstrates contrasting functional organization among both populations,5,6 it is unclear whether the brain can equally learn to control the activity of either class of motor cortex neurons. To answer this question, we used a calcium-imaging-based brain-machine interface (CaBMI)3 and trained different groups of mice to modulate the activity of either IT or PT neurons in order to receive a reward. We found that the animals learned to control PT neuron activity faster and better than IT neuron activity. Moreover, our findings show that the advantage of PT neurons is the result of characteristics inherent to this population as well as their local circuitry and cortical depth location. Taken together, our results suggest that the motor cortex is more efficient at controlling the activity of pyramidal tract neurons, which are embedded deep in the cortex, and relaying motor commands outside the telencephalon.

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.

Assessing transfer entropy from biochemical data

We address the problem of evaluating the transfer entropy (TE) produced by biochemical reactions from experimentally measured data. Although these reactions are generally nonlinear and nonstationary processes making it challenging to achieve accurate modeling, Gaussian approximation can facilitate the TE assessment only by estimating covariance matrices using multiple data obtained from simultaneously measured time series representing the activation levels of biomolecules such as proteins. Nevertheless, the nonstationary nature of biochemical signals makes it difficult to theoretically assess the sampling distributions of TE, which are necessary for evaluating the statistical confidence and significance of the data-driven estimates. We resolve this difficulty by computationally assessing the sampling distributions using techniques from computational statistics. The computational methods are tested by using them in analyzing data generated from a theoretically tractable time-varying signal model, which leads to the development of a method to screen only statistically significant estimates. The usefulness of the developed method is examined by applying it to real biological data experimentally measured from the ERBB-RAS-MAPK system that superintends diverse cell fate decisions. A comparison between cells containing wild-type and mutant proteins exhibits a distinct difference in the time evolution of TE while any apparent difference is hardly found in average profiles of the raw signals. Such a comparison may help in unveiling important pathways of biochemical reactions.

Autonomous inference of complex network dynamics from incomplete and noisy data

The availability of empirical data that capture the structure and behaviour of complex networked systems has been greatly increased in recent years; however, a versatile computational toolbox for unveiling a complex system's nodal and interaction dynamics from data remains elusive. Here we develop a two-phase approach for the autonomous inference of complex network dynamics, and its effectiveness is demonstrated by the tests of inferring neuronal, genetic, social and coupled oscillator dynamics on various synthetic and real networks. Importantly, the approach is robust to incompleteness and noises, including low resolution, observational and dynamical noises, missing and spurious links, and dynamical heterogeneity. We apply the two-phase approach to infer the early spreading dynamics of influenza A flu on the worldwide airline network, and the inferred dynamical equation can also capture the spread of severe acute respiratory syndrome and coronavirus disease 2019. These findings together offer an avenue to discover the hidden microscopic mechanisms of a broad array of real networked systems.

Common network effect-patterns after monoamine reuptake inhibition in dissociated hippocampus cultures

The pharmacological treatment of major depressive disorder with currently available antidepressant drugs is still unsatisfying as response to medication is delayed and in some patients even non-existent. To understand complex psychiatric diseases such as major depressive disorder and their treatment, research focus is shifting from investigating single neurons towards a view of the entire functional and effective neuronal network, because alterations on single synapses through antidepressant drugs may translate to alterations in the entire network. Here, we examined the effects of monoamine reuptake inhibitors on in vitro hippocampal network dynamics using calcium fluorescence imaging and analyzing the data with means of graph theoretical parameters. Hypothesizing that monoamine reuptake inhibitors operate through changes of effective connectivity on micro-scale neuronal networks, we measured the effects of the selective monoamine reuptake inhibitors GBR-12783, Sertraline, Venlafaxine, and Amitriptyline on neuronal networks. We identified a common pattern of effects of the different tested monoamine reuptake inhibitors. After treatment with GBR-12783, Sertraline, and Venlafaxine, the connectivity degree, measuring the number of existing connections in the network, was significantly decreased. All tested substances led to networks with more submodules and a reduced global efficiency. No monoamine reuptake inhibitor did affect network-wide firing rate, the characteristic path length, or the network strength. In our study, we found that monoamine reuptake inhibition in neuronal networks in vitro results in a sharpening of the network structure. These alterations could be the basis for the reorganization of a large-scale miswired network in major depressive disorder.

pH-Dependence of Glucose-Dependent Activity of Beta Cell Networks in Acute Mouse Pancreatic Tissue Slice

Extracellular pH has the potential to affect various aspects of the pancreatic beta cell function. To explain this effect, a number of mechanisms was proposed involving both extracellular and intracellular targets and pathways. Here, we focus on reassessing the influence of extracellular pH on glucose-dependent beta cell activation and collective activity in physiological conditions. To this end we employed mouse pancreatic tissue slices to perform high-temporally resolved functional imaging of cytosolic Ca²⁺ oscillations. We investigated the effect of either physiological H⁺ excess or depletion on the activation properties as well as on the collective activity of beta cell in an islet. Our results indicate that lowered pH invokes activation of a subset of beta cells in substimulatory glucose concentrations, enhances the average activity of beta cells, and alters the beta cell network properties in an islet. The enhanced average activity of beta cells was determined indirectly utilizing cytosolic Ca²⁺ imaging, while direct measuring of insulin secretion confirmed that this enhanced activity is accompanied by a higher insulin release. Furthermore, reduced functional connectivity and higher functional segregation at lower pH, both signs of a reduced intercellular communication, do not necessary result in an impaired insulin release.

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.

Identification of Pattern Completion Neurons in Neuronal Ensembles Using Probabilistic Graphical Models

Neuronal ensembles are groups of neurons with coordinated activity that could represent sensory, motor, or cognitive states. The study of how neuronal ensembles are built, recalled, and involved in the guiding of complex behaviors has been limited by the lack of experimental and analytical tools to reliably identify and manipulate neurons that have the ability to activate entire ensembles. Such pattern completion neurons have also been proposed as key elements of artificial and biological neural networks. Indeed, the relevance of pattern completion neurons is highlighted by growing evidence that targeting them can activate neuronal ensembles and trigger behavior. As a method to reliably detect pattern completion neurons, we use conditional random fields (CRFs), a type of probabilistic graphical model. We apply CRFs to identify pattern completion neurons in ensembles in experiments using in vivo two-photon calcium imaging from primary visual cortex of male mice and confirm the CRFs predictions with two-photon optogenetics. To test the broader applicability of CRFs we also analyze publicly available calcium imaging data (Allen Institute Brain Observatory dataset) and demonstrate that CRFs can reliably identify neurons that predict specific features of visual stimuli. Finally, to explore the scalability of CRFs we apply them to in silico network simulations and show that CRFs-identified pattern completion neurons have increased functional connectivity. These results demonstrate the potential of CRFs to characterize and selectively manipulate neural circuits.SIGNIFICANCE STATEMENT We describe a graph theory method to identify and optically manipulate neurons with pattern completion capability in mouse cortical circuits. Using calcium imaging and two-photon optogenetics in vivo we confirm that key neurons identified by this method can recall entire neuronal ensembles. This method could be broadly applied to manipulate neuronal ensemble activity to trigger behavior or for therapeutic applications in brain prostheses.

Two classes of functional connectivity in dynamical processes in networks

The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines-from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity-one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes-excitations, regular and chaotic oscillators-and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.

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.

Parkinson's disease patient-specific neuronal networks carrying the LRRK2 G2019S mutation unveil early functional alterations that predate neurodegeneration

A deeper understanding of early disease mechanisms occurring in Parkinson’s disease (PD) is needed to reveal restorative targets. Here we report that human induced pluripotent stem cell (iPSC)-derived dopaminergic neurons (DAn) obtained from healthy individuals or patients harboring LRRK2 PD-causing mutation can create highly complex networks with evident signs of functional maturation over time. Compared to control neuronal networks, LRRK2 PD patients’ networks displayed an elevated bursting behavior, in the absence of neurodegeneration. By combining functional calcium imaging, biophysical modeling, and DAn-lineage tracing, we found a decrease in DAn neurite density that triggered overall functional alterations in PD neuronal networks. Our data implicate early dysfunction as a prime focus that may contribute to the initiation of downstream degenerative pathways preceding DAn loss in PD, highlighting a potential window of opportunity for pre-symptomatic assessment of chronic degenerative diseases.

Neuronal Graphs: A Graph Theory Primer for Microscopic, Functional Networks of Neurons Recorded by Calcium Imaging

Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are "graphs"-structures containing objects that are connected. In neuroscience, the objects could be regions of the brain, e.g., fMRI data, or be individual neurons, e.g., calcium imaging with fluorescence microscopy. The formal study of graphs, graph theory, can provide neuroscientists with a large bank of algorithms for exploring networks. Graph theory has already been applied in a variety of ways to fMRI data but, more recently, has begun to be applied at the scales of neurons, e.g., from functional calcium imaging. In this primer we explain the basics of graph theory and relate them to features of microscopic functional networks of neurons from calcium imaging-neuronal graphs. We explore recent examples of graph theory applied to calcium imaging and we highlight some areas where researchers new to the field could go awry.

Embedding optimization reveals long-lasting history dependence in neural spiking activity

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long-potentially redundant-past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.

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.

Inhibitory neurons exhibit high controlling ability in the cortical microconnectome

The brain is a network system in which excitatory and inhibitory neurons keep activity balanced in the highly non-random connectivity pattern of the microconnectome. It is well known that the relative percentage of inhibitory neurons is much smaller than excitatory neurons in the cortex. So, in general, how inhibitory neurons can keep the balance with the surrounding excitatory neurons is an important question. There is much accumulated knowledge about this fundamental question. This study quantitatively evaluated the relatively higher functional contribution of inhibitory neurons in terms of not only properties of individual neurons, such as firing rate, but also in terms of topological mechanisms and controlling ability on other excitatory neurons. We combined simultaneous electrical recording (~2.5 hours) of ~1000 neurons in vitro, and quantitative evaluation of neuronal interactions including excitatory-inhibitory categorization. This study accurately defined recording brain anatomical targets, such as brain regions and cortical layers, by inter-referring MRI and immunostaining recordings. The interaction networks enabled us to quantify topological influence of individual neurons, in terms of controlling ability to other neurons. Especially, the result indicated that highly influential inhibitory neurons show higher controlling ability of other neurons than excitatory neurons, and are relatively often distributed in deeper layers of the cortex. Furthermore, the neurons having high controlling ability are more effectively limited in number than central nodes of k-cores, and these neurons also participate in more clustered motifs. In summary, this study suggested that the high controlling ability of inhibitory neurons is a key mechanism to keep balance with a large number of other excitatory neurons beyond simple higher firing rate. Application of the selection method of limited important neurons would be also applicable for the ability to effectively and selectively stimulate E/I imbalanced disease states.

How small numbers of inhibitory neurons functionally keep balance with large numbers of excitatory neurons in the brain by controlling each other is a fundamental question. Especially, this study quantitatively evaluated a topological mechanism of interaction networks in terms of controlling abilities of individual cortical neurons to other neurons. Combination of simultaneous electrical recording of ~1000 neurons and a quantitative evaluation method of neuronal interactions including excitatory-inhibitory categories, enabled us to evaluate the influence of individual neurons not only about firing rate but also about their relative positions in the networks and controllable ability of other neurons. Especially, the result showed that inhibitory neurons have more controlling ability than excitatory neurons, and such neurons were more often observed in deep layers. Because the limited number of neurons in terms controlling ability were much smaller than neurons based on centrality measure and, of course, more directly selected neurons based on their ability to control other neurons, the selection method of important neurons will help not only to produce realistic computational models but also will help to stimulate brain to effectively treat imbalanced disease states.

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.

Dynamic core-periphery structure of information sharing networks in entorhinal cortex and hippocampus

Neural computation is associated with the emergence, reconfiguration, and dissolution of cell assemblies in the context of varying oscillatory states. Here, we describe the complex spatiotemporal dynamics of cell assemblies through temporal network formalism. We use a sliding window approach to extract sequences of networks of information sharing among single units in hippocampus and entorhinal cortex during anesthesia and study how global and node-wise functional connectivity properties evolve through time and as a function of changing global brain state (theta vs. slow-wave oscillations). First, we find that information sharing networks display, at any time, a core-periphery structure in which an integrated core of more tightly functionally interconnected units links to more loosely connected network leaves. However the units participating to the core or to the periphery substantially change across time windows, with units entering and leaving the core in a smooth way. Second, we find that discrete network states can be defined on top of this continuously ongoing liquid core-periphery reorganization. Switching between network states results in a more abrupt modification of the units belonging to the core and is only loosely linked to transitions between global oscillatory states. Third, we characterize different styles of temporal connectivity that cells can exhibit within each state of the sharing network. While inhibitory cells tend to be central, we show that, otherwise, anatomical localization only poorly influences the patterns of temporal connectivity of the different cells. Furthermore, cells can change temporal connectivity style when the network changes state. Altogether, these findings reveal that the sharing of information mediated by the intrinsic dynamics of hippocampal and entorhinal cortex cell assemblies have a rich spatiotemporal structure, which could not have been identified by more conventional time- or state-averaged analyses of functional connectivity.

It is generally thought that computations performed by local brain circuits rely on complex neural processes, associated with the flexible waxing and waning of cell assemblies, that is, an ensemble of cells firing in tight synchrony. Although cell assembly formation is inherently and unavoidably dynamical, it is still common to find studies in which essentially “static” approaches are used to characterize this process. In the present study, we adopt instead a temporal network approach. Avoiding usual time-averaging procedures, we reveal that hub neurons are not hardwired but that cells vary smoothly their degree of integration within the assembly core. Furthermore, our temporal network framework enables the definition of alternative possible styles of “hubness.” Some cells may share information with a multitude of other units but only in an intermittent manner, as “activists” in a flash mob. In contrast, some other cells may share information in a steadier manner, as resolute “lobbyists.” Finally, by avoiding averages over preimposed states, we show that within each global oscillatory state rich switching dynamics can take place between a repertoire of many available network states. We thus show that the temporal network framework provides a natural and effective language to rigorously describe the rich spatiotemporal patterns of information sharing instantiated by cell assembly evolution.

Electrophysiology Read-Out Tools for Brain-on-Chip Biotechnology

Brain-on-Chip (BoC) biotechnology is emerging as a promising tool for biomedical and pharmaceutical research applied to the neurosciences. At the convergence between lab-on-chip and cell biology, BoC couples in vitro three-dimensional brain-like systems to an engineered microfluidics platform designed to provide an in vivo-like extrinsic microenvironment with the aim of replicating tissue- or organ-level physiological functions. BoC therefore offers the advantage of an in vitro reproduction of brain structures that is more faithful to the native correlate than what is obtained with conventional cell culture techniques. As brain function ultimately results in the generation of electrical signals, electrophysiology techniques are paramount for studying brain activity in health and disease. However, as BoC is still in its infancy, the availability of combined BoC-electrophysiology platforms is still limited. Here, we summarize the available biological substrates for BoC, starting with a historical perspective. We then describe the available tools enabling BoC electrophysiology studies, detailing their fabrication process and technical features, along with their advantages and limitations. We discuss the current and future applications of BoC electrophysiology, also expanding to complementary approaches. We conclude with an evaluation of the potential translational applications and prospective technology developments.

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.

The extended Granger causality analysis for Hodgkin-Huxley neuronal models

How to extract directions of information flow in dynamical systems based on empirical data remains a key challenge. The Granger causality (GC) analysis has been identified as a powerful method to achieve this capability. However, the framework of the GC theory requires that the dynamics of the investigated system can be statistically linearized; i.e., the dynamics can be effectively modeled by linear regressive processes. Under such conditions, the causal connectivity can be directly mapped to the structural connectivity that mediates physical interactions within the system. However, for nonlinear dynamical systems such as the Hodgkin-Huxley (HH) neuronal circuit, the validity of the GC analysis has yet been addressed; namely, whether the constructed causal connectivity is still identical to the synaptic connectivity between neurons remains unknown. In this work, we apply the nonlinear extension of the GC analysis, i.e., the extended GC analysis, to the voltage time series obtained by evolving the HH neuronal network. In addition, we add a certain amount of measurement or observational noise to the time series to take into account the realistic situation in data acquisition in the experiment. Our numerical results indicate that the causal connectivity obtained through the extended GC analysis is consistent with the underlying synaptic connectivity of the system. This consistency is also insensitive to dynamical regimes, e.g., a chaotic or non-chaotic regime. Since the extended GC analysis could in principle be applied to any nonlinear dynamical system as long as its attractor is low dimensional, our results may potentially be extended to the GC analysis in other settings.

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.

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.

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.

Deriving pairwise transfer entropy from network structure and motifs

Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.

Dynamic Tracking Algorithm for Time-Varying Neuronal Network Connectivity using Wide-Field Optical Image Video Sequences

Propagation of signals between neurons and brain regions provides information about the functional properties of neural networks, and thus information transfer. Advances in optical imaging and statistical analyses of acquired optical signals have yielded various metrics for inferring neural connectivity, and hence for mapping signal intercorrelation. However, a single coefficient is traditionally derived to classify the connection strength between two cells, ignoring the fact that neural systems are inherently time-variant systems. To overcome these limitations, we utilized a time-varying Pearson's correlation coefficient, spike-sorting, wavelet transform, and wavelet coherence of calcium transients from DIV 12-15 hippocampal neurons from GCaMP6s mice after applying various concentrations of glutamate. Results provide a comprehensive overview of resulting firing patterns, network connectivity, signal directionality, and network properties. Together, these metrics provide a more comprehensive and robust method of analyzing transient neural signals, and enable future investigations for tracking the effects of different stimuli on network properties.

Improving on transfer entropy-based network reconstruction using time-delays: Approach and validation

Transfer entropy constitutes a viable model-free tool to infer causal relationships between two dynamical systems from their time-series. In an information-theoretic sense, transfer entropy associates a cause-and-effect relationship with directed information transfer, such that one may improve the prediction of the future of a dynamical system from the history of another system. Recent studies have proposed the use of transfer entropy to reconstruct networks, but the inherent dyadic nature of this metric challenges the development of a robust approach that can discriminate direct from indirect interactions between nodes. In this paper, we seek to fill this methodological gap through the cogent integration of time-delays in the transfer entropy computation. By recognizing that information transfer in the network is bound by a finite speed, we relate the value of the time-delayed transfer entropy between two nodes to the number of walks between them. Upon this premise, we lay out the foundation of an alternative framework for network reconstruction, which we illustrate through closed-form results on three-node networks and numerically validate on larger networks, using examples of Boolean models and chaotic maps.

Small-world networks of neuroblastoma cells cultured in three-dimensional polymeric scaffolds featuring multi-scale roughness

Understanding the mechanisms underlying cell-surface interaction is of fundamental importance for the rational design of scaffolds aiming at tissue engineering, tissue repair and neural regeneration applications. Here, we examined patterns of neuroblastoma cells cultured in three-dimensional polymeric scaffolds obtained by two-photon lithography. Because of the intrinsic resolution of the technique, the micrometric cylinders composing the scaffold have a lateral step size of ~200 nm, a surface roughness of around 20 nm, and large values of fractal dimension approaching 2.7. We found that cells in the scaffold assemble into separate groups with many elements per group. After cell wiring, we found that resulting networks exhibit high clustering, small path lengths, and small-world characteristics. These values of the topological characteristics of the network can potentially enhance the quality, quantity and density of information transported in the network compared to equivalent random graphs of the same size. This is one of the first direct observations of cells developing into 3D small-world networks in an artificial matrix.