Signal propagation along unidimensional neuronal networks

Exact solutions for signal propagation along an excitable transmission line

A simple transmission line composed of pulse-coupled units is presented. The model captures the basic properties of excitable media with, in particular, the robust transmission of information via traveling wave solutions. For rectified linear units with a cut-off threshold, the model is exactly solvable and analytical results on propagation are presented. The ability to convey a nontrivial message is studied in detail.

An Overview of In Vitro Biological Neural Networks for Robot Intelligence

In vitro biological neural networks (BNNs) interconnected with robots, so-called BNN-based neurorobotic systems, can interact with the external world, so that they can present some preliminary intelligent behaviors, including learning, memory, robot control, etc. This work aims to provide a comprehensive overview of the intelligent behaviors presented by the BNN-based neurorobotic systems, with a particular focus on those related to robot intelligence. In this work, we first introduce the necessary biological background to understand the 2 characteristics of the BNNs: nonlinear computing capacity and network plasticity. Then, we describe the typical architecture of the BNN-based neurorobotic systems and outline the mainstream techniques to realize such an architecture from 2 aspects: from robots to BNNs and from BNNs to robots. Next, we separate the intelligent behaviors into 2 parts according to whether they rely solely on the computing capacity (computing capacity-dependent) or depend also on the network plasticity (network plasticity-dependent), which are then expounded respectively, with a focus on those related to the realization of robot intelligence. Finally, the development trends and challenges of the BNN-based neurorobotic systems are discussed.

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.

Neuronal circuits overcome imbalance in excitation and inhibition by adjusting connection numbers

The interplay between excitation and inhibition is crucial for neuronal circuitry in the brain. Inhibitory cell fractions in the neocortex and hippocampus are typically maintained at 15 to 30%, which is assumed to be important for stable dynamics. We have studied systematically the role of precisely controlled excitatory/inhibitory (E/I) cellular ratios on network activity using mice hippocampal cultures. Surprisingly, networks with varying E/I ratios maintain stable bursting dynamics. Interburst intervals remain constant for most ratios, except in the extremes of 0 to 10% and 90 to 100% inhibitory cells. Single-cell recordings and modeling suggest that networks adapt to chronic alterations of E/I compositions by balancing E/I connectivity. Gradual blockade of inhibition substantiates the agreement between the model and experiment and defines its limits. Combining measurements of population and single-cell activity with theoretical modeling, we provide a clearer picture of how E/I balance is preserved and where it fails in living neuronal networks.

Improvements of Microcontact Printing for Micropatterned Cell Growth by Contrast Enhancement

Patterned neuronal cell cultures are important tools for investigating neuronal signal integration, network function, and cell-substrate interactions. Because of the variable nature of neuronal cells, the widely used coating method of microcontact printing is in constant need of improvements and adaptations depending on the pattern, cell type, and coating solutions available for a certain experimental system. In this work, we report on three approaches to modify microcontact printing on borosilicate glass surfaces, which we evaluate with contact angle measurements and by determining the quality of patterned neuronal growth. Although background toxification with manganese salt does not result in the desired pattern enhancement, a simple heat treatment of the glass substrates leads to improved background hydrophobicity and therefore neuronal patterning. Thirdly, we extended a microcontact printing process based on covalently linking the glass surface and the coating molecule via an epoxysilane. This extension is an additional hydrophobization step with dodecylamine. We demonstrate that shelf life of the silanized glass is at least 22 weeks, leading to consistently reliable neuronal patterning by microcontact printing. Thus, we compared three practical additions to microcontact printing, two of which can easily be implemented into a workflow for the investigation of patterned neuronal networks.

Propagation of temporal and rate signals in cultured multilayer networks

Analyses of idealized feedforward networks suggest that several conditions have to be satisfied in order for activity to propagate faithfully across layers. Verifying these concepts experimentally has been difficult owing to the vast number of variables that must be controlled. Here, we cultured cortical neurons in a chamber with sequentially connected compartments, optogenetically stimulated individual neurons in the first layer with high spatiotemporal resolution, and then monitored the subthreshold and suprathreshold potentials in subsequent layers. Brief stimuli delivered to the first layer evoked a short-latency transient response followed by sustained activity. Rate signals, carried by the sustained component, propagated reliably through 4 layers, unlike idealized feedforward networks, which tended strongly towards synchrony. Moreover, temporal jitter in the stimulus was transformed into a rate code and transmitted to the last layer. This novel mode of propagation occurred in the balanced excitatory-inhibitory regime and is mediated by NMDA-mediated receptors and recurrent activity.

Analog control with two Artificial Axons

The artificial axon is a recently introduced synthetic assembly of supported lipid bilayers and voltage gated ion channels, displaying the basic electrophysiology of nerve cells. Here we demonstrate the use of two artificial axons as control elements to achieve a simple task. Namely, we steer a remote control car towards a light source, using the sensory input dependent firing rate of the axons as the control signal for turning left or right. We present the result in the form of the analysis of a movie of the car approaching the light source. In general terms, with this work we pursue a constructivist approach to exploring the nexus between machine language at the nerve cell level and behavior.

Assay of Calcium Transients and Synapses in Rat Hippocampal Neurons by Kinetic Image Cytometry and High-Content Analysis: An In Vitro Model System for Postchemotherapy Cognitive Impairment

Postchemotherapy cognitive impairment (PCCI) is commonly exhibited by cancer patients treated with a variety of chemotherapeutic agents, including the endocrine disruptor tamoxifen (TAM). The etiology of PCCI is poorly understood. Our goal was to develop high-throughput assay methods to test the effects of chemicals on neuronal function applicable to PCCI. Rat hippocampal neurons (RHNs) were plated in 96- or 384-well dishes and exposed to test compounds (forskolin [FSK], 17β-estradiol [ES]), TAM or fulvestrant [FUL], aka ICI 182,780) for 6-14 days. Kinetic Image Cytometry™ (KIC™) methods were developed to quantify spontaneously occurring intracellular calcium transients representing the activity of the neurons, and high-content analysis (HCA) methods were developed to quantify the expression, colocalization, and puncta formed by synaptic proteins (postsynaptic density protein-95 [PSD-95] and presynaptic protein Synapsin-1 [Syn-1]). As quantified by KIC, FSK increased the occurrence and synchronization of the calcium transients indicating stimulatory effects on RHN activity, whereas TAM had inhibitory effects. As quantified by HCA, FSK also increased PSD-95 puncta and PSD-95:Syn-1 colocalization, whereas ES increased the puncta of both PSD-95 and Syn-1 with little effect on colocalization. The estrogen receptor antagonist FUL also increased PSD-95 puncta. In contrast, TAM reduced Syn-1 and PSD-95:Syn-1 colocalization, consistent with its inhibitory effects on the calcium transients. Thus TAM reduced activity and synapse formation by the RHNs, which may relate to the ability of this agent to cause PCCI. The results illustrate that KIC and HCA can be used to quantify neurotoxic and neuroprotective effects of chemicals in RHNs to investigate mechanisms and potential therapeutics for PCCI.

Noise focusing in neuronal tissues: Symmetry breaking and localization in excitable networks with quenched disorder

We introduce a coarse-grained stochastic model for the spontaneous activity of neuronal cultures to explain the phenomenon of noise focusing, which entails localization of the noise activity in excitable networks with metric correlations. The system is modeled as a continuum excitable medium with a state-dependent spatial coupling that accounts for the dynamics of synaptic connections. The most salient feature is the emergence at the mesoscale of a vector field V(r), which acts as an advective carrier of the noise. This entails an explicit symmetry breaking of isotropy and homogeneity that stems from the amplification of the quenched fluctuations of the network by the activity avalanches, concomitant with the excitable dynamics. We discuss the microscopic interpretation of V(r) and propose an explicit construction of it. The coarse-grained model shows excellent agreement with simulations at the network level. The generic nature of the observed phenomena is discussed.

External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures

A neuron will fire an action potential when its membrane potential exceeds a certain threshold. In typical activity of the brain, this occurs as a result of chemical inputs to its synapses. However, neurons can also be excited by an imposed electric field. In particular, recent clinical applications activate neurons by creating an electric field externally. It is therefore of interest to investigate how the neuron responds to the external field and what causes the action potential. Fortunately, precise and controlled application of an external electric field is possible for embryonic neuronal cells that are excised, dissociated and grown in cultures. This allows the investigation of these questions in a highly reproducible system. In this paper some of the techniques used for controlled application of external electric field on neuronal cultures are reviewed. The networks can be either one dimensional, i.e. patterned in linear forms or allowed to grow on the whole plane of the substrate, and thus two dimensional. Furthermore, the excitation can be created by the direct application of electric field via electrodes immersed in the fluid (bath electrodes) or by inducing the electric field using the remote creation of magnetic pulses.

Propagation of Collective Temporal Regularity in Noisy Hierarchical Networks

Neuronal communication between different brain areas is achieved in terms of spikes. Consequently, spike-time regularity is closely related to many cognitive tasks and timing precision of neural information processing. A recent experiment on primate parietal cortex reports that spike-time regularity increases consistently from primary sensory to higher cortical regions. This observation conflicts with the influential view that spikes in the neocortex are fundamentally irregular. To uncover the underlying network mechanism, we construct a multilayered feedforward neural information transmission pathway and investigate how spike-time regularity evolves across subsequent layers. Numerical results reveal that despite the obviously irregular spiking patterns in previous several layers, neurons in downstream layers can generate rather regular spikes, which depends on the network topology. In particular, we find that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight, i.e., the optimal topology parameter maximizes the spike-timing regularity. Furthermore, it is demonstrated that synaptic properties, including inhibition, synaptic transient dynamics, and plasticity, have significant impacts on spike-timing regularity propagation. The emergence of the increasingly regular spiking (RS) patterns in higher parietal regions can, thus, be viewed as a natural consequence of spiking activity propagation between different brain areas. Finally, we validate an important function served by increased RS: promoting reliable propagation of spike-rate signals across downstream layers.

Anesthetic Sevoflurane Causes Rho-Dependent Filopodial Shortening in Mouse Neurons

Early postnatal anesthesia causes long-lasting learning and memory impairment in rodents, however, evidence for a specific neurotoxic effect on early synaptogenesis has not been demonstrated. Drebrin A is an actin binding protein whose localization in dendritic protrusions serves an important role in dendritic spine morphogenesis, and is a marker for early synaptogenesis. We therefore set out to investigate whether clinically-relevant concentrations of anesthetic sevoflurane, widely- used in infants and children, alters dendritic morphology in cultured fetal day 16 mouse hippocampal neurons. After 7 days in vitro, mouse hippocampal neurons were exposed to four hours of 3% sevoflurane in 95% air/5% CO₂ or control condition (95% air/5% CO₂). Neurons were fixed in 4% paraformaldehyde and stained with Alexa Fluor555-Phalloidin, and/or rabbit anti-mouse drebrin A/E antibodies which permitted subcellular localization of filamentous (F)-actin and/or drebrin immunoreactivity, respectively. Sevoflurane caused acute significant length-shortening in filopodia and thin dendritic spines in days-in-vitro 7 neurons, an effect which was completely rescued by co-incubating neurons with ten micromolar concentrations of the selective Rho kinase inhibitor Y27632. Filopodia and thin spine recovered in length two days after sevoflurane exposure. Yet cluster-type filopodia (a precursor to synaptic filopodia) were persistently significantly decreased in number on day-in-vitro 9, in part owing to preferential localization of drebrin immunoreactivity to dendritic shafts versus filopodial stalks. These data suggest that sevoflurane induces F-actin depolymerization leading to acute, reversible length-shortening in dendritic protrusions through a mechanism involving (in part) activation of RhoA/Rho kinase signaling and impairs localization of drebrin A to filopodia required for early excitatory synapse formation.

Signal Propagation between Neuronal Populations Controlled by Micropatterning

The central nervous system consists of an unfathomable number of functional networks enabling highly sophisticated information processing. Guided neuronal growth with a well-defined connectivity and accompanying polarity is essential for the formation of these networks. To investigate how two-dimensional protein patterns influence neuronal outgrowth with respect to connectivity and functional polarity between adjacent populations of neurons, a microstructured model system was established. Exclusive cell growth on patterned substrates was achieved by transferring a mixture of poly-l-lysine and laminin to a cell-repellent glass surface by microcontact printing. Triangular structures with different opening angle, height, and width were chosen as a pattern to achieve network formation with defined behavior at the junction of adjacent structures. These patterns were populated with dissociated primary cortical embryonic rat neurons and investigated with respect to their impact on neuronal outgrowth by immunofluorescence analysis, as well as their functional connectivity by calcium imaging. Here, we present a highly reproducible technique to devise neuronal networks in vitro with a predefined connectivity induced by the design of the gateway. Daisy-chained neuronal networks with predefined connectivity and functional polarity were produced using the presented micropatterning method. Controlling the direction of signal propagation among populations of neurons provides insights to network communication and offers the chance to investigate more about learning processes in networks by external manipulation of cells and signal cascades.

Structure, Function, and Propagation of Information across Living Two, Four, and Eight Node Degree Topologies

In this study, we created four network topologies composed of living cortical neurons and compared resultant structural-functional dynamics including the nature and quality of information transmission. Each living network was composed of living cortical neurons and were created using microstamping of adhesion promoting molecules and each was "designed" with different levels of convergence embedded within each structure. Networks were cultured over a grid of electrodes that permitted detailed measurements of neural activity at each node in the network. Of the topologies we tested, the "Random" networks in which neurons connect based on their own intrinsic properties transmitted information embedded within their spike trains with higher fidelity relative to any other topology we tested. Within our patterned topologies in which we explicitly manipulated structure, the effect of convergence on fidelity was dependent on both topology and time-scale (rate vs. temporal coding). A more detailed examination using tools from network analysis revealed that these changes in fidelity were also associated with a number of other structural properties including a node's degree, degree-degree correlations, path length, and clustering coefficients. Whereas information transmission was apparent among nodes with few connections, the greatest transmission fidelity was achieved among the few nodes possessing the highest number of connections (high degree nodes or putative hubs). These results provide a unique view into the relationship between structure and its affect on transmission fidelity, at least within these small neural populations with defined network topology. They also highlight the potential role of tools such as microstamp printing and microelectrode array recordings to construct and record from arbitrary network topologies to provide a new direction in which to advance the study of structure-function relationships.

Involvement of Potassium and Cation Channels in Hippocampal Abnormalities of Embryonic Ts65Dn and Tc1 Trisomic Mice

Down syndrome (DS) mouse models exhibit cognitive deficits, and are used for studying the neuronal basis of DS pathology. To understand the differences in the physiology of DS model neurons, we used dissociated neuronal cultures from the hippocampi of Ts65Dn and Tc1 DS mice. Imaging of [Ca²⁺]i and whole cell patch clamp recordings were used to analyze network activity and single neuron properties, respectively. We found a decrease of ~ 30% in both fast (A-type) and slow (delayed rectifier) outward potassium currents. Depolarization of Ts65Dn and Tc1 cells produced fewer spikes than diploid cells. Their network bursts were smaller and slower than diploids, displaying a 40% reduction in Δf / f₀ of the calcium signals, and a 30% reduction in propagation velocity. Additionally, Ts65Dn and Tc1 neurons exhibited changes in the action potential shape compared to diploid neurons, with an increase in the amplitude of the action potential, a lower threshold for spiking, and a sharp decrease of about 65% in the after-hyperpolarization amplitude.

Numerical simulations reproduced the DS measured phenotype by variations in the conductance of the delayed rectifier and A-type, but necessitated also changes in inward rectifying and M-type potassium channels and in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels. We therefore conducted whole cell patch clamp measurements of M-type potassium currents, which showed a ~ 90% decrease in Ts65Dn neurons, while HCN measurements displayed an increase of ~ 65% in Ts65Dn cells. Quantitative real-time PCR analysis indicates overexpression of 40% of KCNJ15, an inward rectifying potassium channel, contributing to the increased inhibition. We thus find that changes in several types of potassium channels dominate the observed DS model phenotype.

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Down syndrome model neurons display altered action potential shape, are less excitable and have decreased potassium currents.

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The data is accurately described by a numerical simulation that changes conductance of four potassium and the HCN currents.

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Measurements of the currents related to these four channels, and RT-pcr for a fifth (KCNJ15), confirm the numerical model.

In Down syndrome (DS) cognitive function is impaired, leading us to use cultured hippocampal neuronal networks to investigate the cellular basis of its pathology. DS mouse model neurons are less excitable, produce fewer spikes and generate less network activity. Alterations in several types of potassium currents were detected in these neurons. Numerical simulation of a DS neuron successfully reproduced the experimental results. Beyond extending our understanding of neuronal function and pathology, the alterations in channel conductance can now be targeted with specific drugs so as to point to new directions in therapy of cognitive disabilities of DS.

Chronaxie Measurements in Patterned Neuronal Cultures from Rat Hippocampus

Excitation of neurons by an externally induced electric field is a long standing question that has recently attracted attention due to its relevance in novel clinical intervention systems for the brain. Here we use patterned quasi one-dimensional neuronal cultures from rat hippocampus, exploiting the alignment of axons along the linear patterned culture to separate the contribution of dendrites to the excitation of the neuron from that of axons. Network disconnection by channel blockers, along with rotation of the electric field direction, allows the derivation of strength-duration (SD) curves that characterize the statistical ensemble of a population of cells. SD curves with the electric field aligned either parallel or perpendicular to the axons yield the chronaxie and rheobase of axons and dendrites respectively, and these differ considerably. Dendritic chronaxie is measured to be about 1 ms, while that of axons is on the order of 0.1 ms. Axons are thus more excitable at short time scales, but at longer time scales dendrites are more easily excited. We complement these studies with experiments on fully connected cultures. An explanation for the chronaxie of dendrites is found in the numerical simulations of passive, realistically structured dendritic trees under external stimulation. The much shorter chronaxie of axons is not captured in the passive model and may be related to active processes. The lower rheobase of dendrites at longer durations can improve brain stimulation protocols, since in the brain dendrites are less specifically oriented than axonal bundles, and the requirement for precise directional stimulation may be circumvented by using longer duration fields.

An in vitro method to manipulate the direction and functional strength between neural populations

We report the design and application of a Micro Electro Mechanical Systems (MEMs) device that permits investigators to create arbitrary network topologies. With this device investigators can manipulate the degree of functional connectivity among distinct neural populations by systematically altering their geometric connectivity in vitro. Each polydimethylsilxane (PDMS) device was cast from molds and consisted of two wells each containing a small neural population of dissociated rat cortical neurons. Wells were separated by a series of parallel micrometer scale tunnels that permitted passage of axonal processes but not somata; with the device placed over an 8 × 8 microelectrode array, action potentials from somata in wells and axons in microtunnels can be recorded and stimulated. In our earlier report we showed that a one week delay in plating of neurons from one well to the other led to a filling and blocking of the microtunnels by axons from the older well resulting in strong directionality (older to younger) of both axon action potentials in tunnels and longer duration and more slowly propagating bursts of action potentials between wells. Here we show that changing the number of tunnels, and hence the number of axons, connecting the two wells leads to changes in connectivity and propagation of bursting activity. More specifically, the greater the number of tunnels the stronger the connectivity, the greater the probability of bursting propagating between wells, and shorter peak-to-peak delays between bursts and time to first spike measured in the opposing well. We estimate that a minimum of 100 axons are needed to reliably initiate a burst in the opposing well. This device provides a tool for researchers interested in understanding network dynamics who will profit from having the ability to design both the degree and directionality connectivity among multiple small neural populations.

Combining microfluidics, optogenetics and calcium imaging to study neuronal communication in vitro

In this paper we report the combination of microfluidics, optogenetics and calcium imaging as a cheap and convenient platform to study synaptic communication between neuronal populations in vitro. We first show that Calcium Orange indicator is compatible in vitro with a commonly used Channelrhodopsine-2 (ChR2) variant, as standard calcium imaging conditions did not alter significantly the activity of transduced cultures of rodent primary neurons. A fast, robust and scalable process for micro-chip fabrication was developed in parallel to build micro-compartmented cultures. Coupling optical fibers to each micro-compartment allowed for the independent control of ChR2 activation in the different populations without crosstalk. By analyzing the post-stimuli activity across the different populations, we finally show how this platform can be used to evaluate quantitatively the effective connectivity between connected neuronal populations.

A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination

Epilepsy--the condition of recurrent, unprovoked seizures--manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination.

Oscillation-induced signal transmission and gating in neural circuits

Reliable signal transmission constitutes a key requirement for neural circuit function. The propagation of synchronous pulse packets through recurrent circuits is hypothesized to be one robust form of signal transmission and has been extensively studied in computational and theoretical works. Yet, although external or internally generated oscillations are ubiquitous across neural systems, their influence on such signal propagation is unclear. Here we systematically investigate the impact of oscillations on propagating synchrony. We find that for standard, additive couplings and a net excitatory effect of oscillations, robust propagation of synchrony is enabled in less prominent feed-forward structures than in systems without oscillations. In the presence of non-additive coupling (as mediated by fast dendritic spikes), even balanced oscillatory inputs may enable robust propagation. Here, emerging resonances create complex locking patterns between oscillations and spike synchrony. Interestingly, these resonances make the circuits capable of selecting specific pathways for signal transmission. Oscillations may thus promote reliable transmission and, in co-action with dendritic nonlinearities, provide a mechanism for information processing by selectively gating and routing of signals. Our results are of particular interest for the interpretation of sharp wave/ripple complexes in the hippocampus, where previously learned spike patterns are replayed in conjunction with global high-frequency oscillations. We suggest that the oscillations may serve to stabilize the replay.

Rhythmic activity in the brain is ubiquitous, its functions are debated. Here we show that it may contribute to the reliable transmission of information within brain areas. We find that its effect is particularly strong if we take nonlinear coupling into account. This experimentally found neuronal property implies that inputs which arrive nearly simultaneously can have a much stronger impact than expected from the sum of their individuals strengths. In such systems, rhythmic activity supports information transmission even if its positive and negative part exactly cancels all the time. Further, the information transmission can adapt to the oscillation frequency to optimally benefit from it. Finally, we show that rhythms with different frequencies may enable or disable communication channels, and are thus suitable for the steering of information flow.

Micropatterned substrates coated with neuronal adhesion molecules for high-content study of synapse formation

Studying the roles of different proteins and the mechanisms involved in synaptogenesis is hindered by the complexity and heterogeneity of synapse types, and by the spatial and temporal unpredictability of spontaneous synapse formation. Here we demonstrate a robust and high-content method to induce selectively presynaptic or postsynaptic structures at controlled locations. Neurons are cultured on micropatterned substrates comprising arrays of micron-scale dots coated with various synaptogenic adhesion molecules. When plated on neurexin-1β-coated micropatterns, neurons expressing neuroligin-1 exhibit specific dendritic organization and selective recruitment of the postsynaptic scaffolding molecule PSD-95. Furthermore, functional AMPA receptors are trapped at neurexin-1β dots, as revealed by live-imaging experiments. In contrast, neurons plated on SynCAM1-coated substrates exhibit strongly patterned axons and selectively assemble functional presynapses. N-cadherin coating, however, is not able to elicit synapses, indicating the specificity of our system. This method opens the way to both fundamental and therapeutic studies of various synaptic systems.

Propagating synchrony in feed-forward networks

Coordinated patterns of precisely timed action potentials (spikes) emerge in a variety of neural circuits but their dynamical origin is still not well understood. One hypothesis states that synchronous activity propagating through feed-forward chains of groups of neurons (synfire chains) may dynamically generate such spike patterns. Additionally, synfire chains offer the possibility to enable reliable signal transmission. So far, mostly densely connected chains, often with all-to-all connectivity between groups, have been theoretically and computationally studied. Yet, such prominent feed-forward structures have not been observed experimentally. Here we analytically and numerically investigate under which conditions diluted feed-forward chains may exhibit synchrony propagation. In addition to conventional linear input summation, we study the impact of non-linear, non-additive summation accounting for the effect of fast dendritic spikes. The non-linearities promote synchronous inputs to generate precisely timed spikes. We identify how non-additive coupling relaxes the conditions on connectivity such that it enables synchrony propagation at connectivities substantially lower than required for linearly coupled chains. Although the analytical treatment is based on a simple leaky integrate-and-fire neuron model, we show how to generalize our methods to biologically more detailed neuron models and verify our results by numerical simulations with, e.g., Hodgkin Huxley type neurons.

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

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.

Enhancement of neural representation capacity by modular architecture in networks of cortical neurons

Biological networks are ubiquitously modular, a feature that is believed to be essential for the enhancement of their functional capacities. Here, we have used a simple modular in vitro design to examine the possibility that modularity enhances network functionality in the context of input representation. We cultured networks of cortical neurons obtained from newborn rats in vitro on substrate-integrated multi-electrode arrays, forcing the network to develop two well-defined modules of neural populations that are coupled by a narrow canal. We measured the neural activity, and examined the capacity of each module to individually classify (i.e. represent) spatially distinct electrical stimuli and propagate input-specific activity features to their downstream coupled counterpart. We show that, although each of the coupled modules maintains its autonomous functionality, a significant enhancement of representational capacity is achieved when the system is observed as a whole. We interpret our results in terms of a relative decorrelation effect imposed by weak coupling between modules.

Response of traveling waves to transient inputs in neural fields

We analyze the effects of transient stimulation on traveling waves in neural field equations. Neural fields are modeled as integro-differential equations whose convolution term represents the synaptic connections of a spatially extended neuronal network. The adjoint of the linearized wave equation can be used to identify how a particular input will shift the location of a traveling wave. This wave response function is analogous to the phase response curve of limit cycle oscillators. For traveling fronts in an excitatory network, the sign of the shift depends solely on the sign of the transient input. A complementary estimate of the effective shift is derived using an equation for the time-dependent speed of the perturbed front. Traveling pulses are analyzed in an asymmetric lateral inhibitory network and they can be advanced or delayed, depending on the position of spatially localized transient inputs. We also develop bounds on the amplitude of transient input necessary to terminate traveling pulses, based on the global bifurcation structure of the neural field.

Ring-shaped neuronal networks: a platform to study persistent activity

Persistent activity in the brain is involved in working memory and motor planning. The ability of the brain to hold information 'online' long after an initiating stimulus is a hallmark of brain areas such as the prefrontal cortex. Recurrent network loops such as the thalamocortical loop and reciprocal loops in the cortex are potential substrates that can support such activity. However, native brain circuitry makes it difficult to study mechanisms underlying such persistent activity. Here we propose a platform to study synaptic mechanisms of such persistent activity by constraining neuronal networks to a recurrent loop like geometry. Using a polymer stamping technique, adhesive proteins are transferred onto glass substrates in a precise ring shape. Primary rat hippocampal cultures were capable of forming ring-shaped networks containing 40-60 neurons. Calcium imaging of these networks show evoked persistent activity in an all-or-none manner. Blocking inhibition with bicuculline methaiodide (BMI) leads to an increase in the duration of persistent activity. These persistent phases were abolished by blockade of asynchronous neurotransmitter release by ethylene glycol tetraacetic acid (EGTA-AM).

BDNF and NT-3 Increase Velocity of Activity Front Propagation in Unidimensional Hippocampal Cultures

Neurotrophins are known to promote synapse development as well as to regulate the efficacy of mature synapses. We have previously reported that in two-dimensional rat hippocampal cultures, brain-derived neurotrophic factor (BDNF) and neurotrophin-3 significantly increase the number of excitatory input connections. Here we measure the effect of these neurotrophic agents on propagating fronts that arise spontaneously in quasi-one-dimensional rat hippocampal cultures. We observe that chronic treatment with BDNF increased the velocity of the propagation front by about 30%. This change is attributed to an increase in the excitatory input connectivity. We analyze the experiment using the Feinerman–Golomb/Ermentrout–Jacobi/Moses–Osan model for the propagation of fronts in a one-dimensional neuronal network with synaptic delay and introduce the synaptic connection probability between adjacent neurons as a new parameter of the model. We conclude that BDNF increases the number of excitatory connections by favoring the probability to form connections between neurons, but without significantly modifying the range of the connections (connectivity footprint).

Leaders of neuronal cultures in a quorum percolation model

We present a theoretical framework using quorum percolation for describing the initiation of activity in a neural culture. The cultures are modeled as random graphs, whose nodes are excitatory neurons with k_in inputs and k_out outputs, and whose input degrees k_in = k obey given distribution functions p_k. We examine the firing activity of the population of neurons according to their input degree (k) classes and calculate for each class its firing probability Φ_k(t) as a function of t. The probability of a node to fire is found to be determined by its in-degree k, and the first-to-fire neurons are those that have a high k. A small minority of high-k-classes may be called “Leaders,” as they form an interconnected sub-network that consistently fires much before the rest of the culture. Once initiated, the activity spreads from the Leaders to the less connected majority of the culture. We then use the distribution of in-degree of the Leaders to study the growth rate of the number of neurons active in a burst, which was experimentally measured to be initially exponential. We find that this kind of growth rate is best described by a population that has an in-degree distribution that is a Gaussian centered around k = 75 with width σ = 31 for the majority of the neurons, but also has a power law tail with exponent −2 for 10% of the population. Neurons in the tail may have as many as k = 4,700 inputs. We explore and discuss the correspondence between the degree distribution and a dynamic neuronal threshold, showing that from the functional point of view, structure and elementary dynamics are interchangeable. We discuss possible geometric origins of this distribution, and comment on the importance of size, or of having a large number of neurons, in the culture.

Neuronal density determines network connectivity and spontaneous activity in cultured hippocampus

The effects of neuronal density on morphological and functional attributes of the evolving networks were studied in cultured dissociated hippocampal neurons. Plating at different densities affected connectivity among the neurons, such that sparse networks exhibited stronger synaptic connections between pairs of recorded neurons. This was associated with different patterns of spontaneous network activity with enhanced burst size but reduced burst frequency in the sparse cultures. Neuronal density also affected the morphology of the dendrites and spines of these neurons, such that sparse neurons had a simpler dendritic tree and fewer dendritic spines. Additionally, analysis of neurons transfected with PSD95 revealed that in sparse cultures the synapses are formed on the dendritic shaft, whereas in dense cultures the synapses are formed primarily on spine heads. These experiments provide important clues on the role of neuronal density in population activity and should yield new insights into the rules governing neuronal network connectivity.

BDNF and NT-3 increase excitatory input connectivity in rat hippocampal cultures

The neurotrophic factors brain-derived neurotrophic factor (BDNF) and neurotrophin-3 (NT-3) have been shown to promote excitatory and inhibitory synapse development. However, a quantitative analysis of their influence on connectivity has proven in general difficult to achieve. In this work we use a novel experimental approach based on percolation concepts that provides a quantification of the average number of connections per neuron. In combination with electrophysiological measurements, we characterize the changes in network connectivity induced by BDNF and NT-3 in rat hippocampal cultures. We show that, on the one hand, BDNF and NT-3 accelerate the maturation of connectivity in the network by about 17 h. On the other hand, BDNF and NT-3 increase the number of excitatory input connections by a factor of about two, but without modifying the number of inhibitory input connections. This scenario of a dominant effect on the excitation is supported by the analysis of spontaneous population bursts in cultures treated with either BDNF or NT-3, which show burst amplitudes that are insensitive to the blockade of inhibition. A leaky integrate-and-fire model reproduces the experimental results well.

Determinants of spontaneous activity in networks of cultured hippocampus

The brain generates extensive spontaneous network activity patterns, even in the absence of extrinsic afferents. While the cognitive correlates of these complex activities are being unraveled, the rules that govern the generation, synchronization and spread of different patterns of intrinsic network activity in the brain are still enigmatic. Using hippocampal neurons grown in dissociated cultures, we are able to study these rules. Network activity emerges at 3-7 days in-vitro (DIV) independent of either ongoing excitatory or inhibitory synaptic activity. Network activity matures over the following several weeks in culture, when it becomes sensitive to chronic drug treatment. The size of the network determines its properties, such that dense networks have higher rates of less synchronized activity than that of sparse networks, which are more synchronized but rhythm at lower rates. Large networks cannot be triggered to fire by activating a single neuron. Small networks, on the other hand, do not burst spontaneously, but can be made to discharge a network burst by stimulating a single neuron. Thus, the strength of connectivity is inversely correlated with spontaneous activity and synchronicity. In the absence of confirmed 'leader' neurons, synchronous bursting network activity appears to be triggered by at least several local subthreshold synaptic events. We conclude that networks of neurons in culture can produce spontaneous synchronized activity and serve as a viable model system for the analysis of the rules that govern network activity in the brain.

Magnetic stimulation of one-dimensional neuronal cultures

Transcranial magnetic stimulation is a remarkable tool for neuroscience research, with a multitude of diagnostic and therapeutic applications. Surprisingly, application of the same magnetic stimulation directly to neurons that are dissected from the brain and grown in vitro was not reported to activate them to date. Here we report that central nervous system neurons patterned on large enough one-dimensional rings can be magnetically stimulated in vitro. In contrast, two-dimensional cultures with comparable size do not respond to excitation. This happens because the one-dimensional pattern enforces an ordering of the axons along the ring, which is designed to follow the lines of the magnetically induced electric field. A small group of sensitive (i.e., initiating) neurons respond even when the network is disconnected, and are presumed to excite the entire network when it is connected. This implies that morphological and electrophysiological properties of single neurons are crucial for magnetic stimulation. We conjecture that the existence of a select group of neurons with higher sensitivity may occur in the brain in vivo as well, with consequences for transcranial magnetic stimulation.

Towards neuro-memory-chip: imprinting multiple memories in cultured neural networks

We show that using local chemical stimulations it is possible to imprint persisting (days) multiple memories (collective modes of neuron firing) in the activity of cultured neural networks. Microdroplets of inhibitory antagonist are injected at a location selected based on real-time analysis of the recorded activity. The neurons at the stimulated locations turn into a focus for initiating synchronized bursting events (the collective modes) each with its own specific spatiotemporal pattern of neuron firing.

Variability and corresponding amplitude-velocity relation of activity propagating in one-dimensional neural cultures

We investigate the propagation of neural activity along one-dimensional rat hippocampal cultures patterned in lines over multielectrode arrays. Activity occurs spontaneously or is evoked by local electrical or chemical stimuli, with different resulting propagation velocities and firing rate amplitudes. A variability of an order of magnitude in velocity and amplitude is observed in spontaneous activity. A linear relation between velocity and amplitude is identified. We define a measure for neuron activation synchrony and find that it correlates with front velocity and is higher for electrically evoked fronts. We present a model that explains the linear relation between amplitude and velocity, which highlights the role of synchrony. The relation to current models for signal propagation in neural media is discussed.

Identification and dynamics of spontaneous burst initiation zones in unidimensional neuronal cultures

Spontaneous activity is typical of in vitro neural networks, often in the form of large population bursts. The origins of this activity are attributed to intrinsically bursting neurons and to noisy backgrounds as well as to recurrent network connections. Spontaneous activity is often observed to emanate from localized sources or initiation zones, propagating from there to excite large populations of neurons. In this study, we use unidimensional cultures to overcome experimental difficulties in identifying initiation zones in vivo and in dissociated two-dimensional cultures. We found that spontaneous activity in these cultures is initiated exclusively in localized zones that are characterized by high neuronal density but also by recurrent and inhibitory network connections. We demonstrate that initiation zones compete in driving network activity in a winner-takes-most scenario.

Abstracts of the 15th Annual Meeting of the Israel Society for Neuroscience (Eilat, Israel, December 3–5, 2006)

The Israel Society for Neuroscience (ISFN) was founded in 1993 by a group of Israeli leading scientists conducting research in the area of neurobiology. The primary goal of the society was to promote and disseminate the knowledge and understanding acquired by its members, and to strengthen interactions between them. Since then, the society holds its annual meeting every year in Eilat during the month of December. At these annual meetings the senior Israeli neurobiologists, their teams, and their graduate students, as well as foreign scientists and students, present their recent research findings in platform and poster presentations. The meeting also offers the opportunity for the researchers to exchange information with each other, often leading to the initiation of collaborative studies. Both the number of members of the society and of those participating in the annual meeting is constantly increasing, and it is anticipated that this year about 600 scientists will convene at the Princess Hotel in Eilat, Israel.

Further information concerning the Israel Society for Neuroscience can be found at http://www.isfn.org.il.

Committee:

Zvi Wollberg (President) Tel Aviv University

Edi Barkai University of Haifa

Etti Grauer Israel Institute for Biological Research, Ness Ziona

Yoram Rami Grossman Ben Gurion University of the Negev

Yoel Yaari Hebrew University of Jerusalem

Gal Yadid Bar-Ilan University

Shlomo Rotshenker (President Elect) Hebrew University of Jerusalem

Ettie Grauer (Treasurer) Israel Institute for Biological Research, Ness Ziona

Michal Gilady (Administrator) Rishon Le Zion

Percolation in living neural networks

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with an exponent beta approximately or = 0.65. Beta is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is Gaussian rather than scale free.

Transport of information along unidimensional layered networks of dissociated hippocampal neurons and implications for rate coding

The ability of synchronous population activity in layered networks to transmit a rate code is a focus of recent debate. We investigate these issues using a patterned unidimensional hippocampal culture. The network exhibits population bursts that travel its full length, with the advantage that signals propagate along a clearly defined path. The amplitudes of activity are measured using calcium imaging, a good approximate of population rate code, and the distortion of the signal as it travels is analyzed. We demonstrate that propagation along the line is precisely described by information theory as a chain of Gaussian communication channels. The balance of excitatory and inhibitory synapses is crucial for this transmission. However, amplitude information carried along this layered neuronal structure fails within 3 mm, approximately 10 mean axon lengths, and is limited by noise in the synaptic transmission. We conclude that rate codes cannot be reliably transmitted through long layered networks.