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

Deepening the role of excitation/inhibition balance in human iPSCs-derived neuronal networks coupled to MEAs during long-term development

Objective.The purpose of this study is to investigate whether and how the balance between excitation and inhibition ('E/I balance') influences the spontaneous development of human-derived neuronal networksin vitro. To achieve that goal, we performed a long-term (98 d) characterization of both homogeneous (only excitatory or inhibitory neurons) and heterogeneous (mixed neuronal types) cultures with controlled E/I ratios (i.e. E:I 0:100, 25:75, 50:50, 75:25, 100:0) by recording their electrophysiological activity using micro-electrode arrays.Approach.Excitatory and inhibitory neurons were derived from human induced pluripotent stem cells (hiPSCs). We realized five different configurations by systematically varying the glutamatergic and GABAergic percentages.Main results.We successfully built both homogeneous and heterogeneous neuronal cultures from hiPSCs finely controlling the E/I ratios; we were able to maintain them for up to 3 months. Homogeneity differentially impacted purely inhibitory (no bursts) and purely excitatory (few bursts) networks, deviating from the typical traits of heterogeneous cultures (burst dominated). Increased inhibition in heterogeneous cultures strongly affected the duration and organization of bursting and network bursting activity. Spike-based functional connectivity and image-based deep learning analysis further confirmed all the above.Significance.Healthy neuronal activity is controlled by a well-defined E/I balance whose alteration could lead to the onset of neurodevelopmental disorders like schizophrenia or epilepsy. Most of the commonly usedin vitromodels are animal-derived or too simplified and thus far from thein vivohuman condition. In this work, by performing a long-term study of hiPSCs-derived neuronal networks obtained from healthy human subjects, we demonstrated the feasibility of a robustin vitromodel which can be further exploited for investigating pathological conditions where the E/I balance is impaired.

Modeling the three-dimensional connectivity of in vitro cortical ensembles coupled to Micro-Electrode Arrays

Nowadays, in vitro three-dimensional (3D) neuronal networks are becoming a consolidated experimental model to overcome most of the intrinsic limitations of bi-dimensional (2D) assemblies. In the 3D environment, experimental evidence revealed a wider repertoire of activity patterns, characterized by a modulation of the bursting features, than the one observed in 2D cultures. However, it is not totally clear and understood what pushes the neuronal networks towards different dynamical regimes. One possible explanation could be the underlying connectivity, which could involve a larger number of neurons in a 3D rather than a 2D space and could organize following well-defined topological schemes. Driven by experimental findings, achieved by recording 3D cortical networks organized in multi-layered structures coupled to Micro-Electrode Arrays (MEAs), in the present work we developed a large-scale computational network model made up of leaky integrate-and-fire (LIF) neurons to investigate possible structural configurations able to sustain the emerging patterns of electrophysiological activity. In particular, we investigated the role of the number of layers defining a 3D assembly and the spatial distribution of the connections within and among the layers. These configurations give rise to different patterns of activity that could be compared to the ones emerging from real in vitro 3D neuronal populations. Our results suggest that the introduction of three-dimensionality induced a global reduction in both firing and bursting rates with respect to 2D models. In addition, we found that there is a minimum number of layers necessary to obtain a change in the dynamics of the network. However, the effects produced by a 3D organization of the cells is somewhat mitigated if a scale-free connectivity is implemented in either one or all the layers of the network. Finally, the best matching of the experimental data is achieved supposing a 3D connectivity organized in structured bundles of links located in different areas of the 2D network.

Modularity and neuronal heterogeneity: Two properties that influence in vitro neuropharmacological experiments

Introduction

The goal of this work is to prove the relevance of the experimental model (in vitro neuronal networks in this study) when drug-delivery testing is performed.

Methods

We used dissociated cortical and hippocampal neurons coupled to Micro-Electrode Arrays (MEAs) arranged in different configurations characterized by modularity (i.e., the presence of interconnected sub-networks) and heterogeneity (i.e., the co-existence of neurons coming from brain districts). We delivered increasing concentrations of bicuculline (BIC), a neuromodulator acting on the GABAergic system, and we extracted the IC₅₀ values (i.e., the effective concentration yielding a reduction in the response by 50%) of the mean firing rate for each configuration.

Results

We found significant lower values of the IC₅₀ computed for modular cortical-hippocampal ensembles than isolated cortical or hippocampal ones.

Discussion

Although tested with a specific neuromodulator, this work aims at proving the relevance of ad hoc experimental models to perform neuropharmacological experiments to avoid errors of overestimation/underestimation leading to biased information in the characterization of the effects of a drug on neuronal networks.

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 avalanche dynamics and functional connectivity elucidate information propagation in vitro

Cascading activity is commonly observed in complex dynamical systems, including networks of biological neurons, and how these cascades spread through the system is reliant on how the elements of the system are connected and organized. In this work, we studied networks of neurons as they matured over 50 days in vitro and evaluated both their dynamics and their functional connectivity structures by observing their electrophysiological activity using microelectrode array recordings. Correlations were obtained between features of their activity propagation and functional connectivity characteristics to elucidate the interplay between dynamics and structure. The results indicate that in vitro networks maintain a slightly subcritical state by striking a balance between integration and segregation. Our work demonstrates the complementarity of these two approaches—functional connectivity and avalanche dynamics—in studying information propagation in neurons in vitro, which can in turn inform the design and optimization of engineered computational substrates.

Functional Inhibitory Connections Modulate the Electrophysiological Activity Patterns of Cortical-Hippocampal Ensembles

The brain is a complex organ composed of billions of neurons connected through excitatory and inhibitory synapses. Its structure reveals a modular topological organization, where neurons are arranged in interconnected assemblies. The generated patterns of electrophysiological activity are shaped by two main factors: network heterogeneity and the topological properties of the underlying connectivity that strongly push the dynamics toward different brain-states. In this work, we exploited an innovative polymeric structure coupled to Micro-Electrode Arrays (MEAs) to recreate in vitro heterogeneous interconnected (modular) neuronal networks made up of cortical and hippocampal neurons. We investigated the propagation of spike sequences between the two interconnected subpopulations during the networks' development, correlating functional and structural connectivity to dynamics. The simultaneous presence of two neuronal types shaped the features of the functional connections (excitation vs. inhibition), orchestrating the emerging patterns of electrophysiological activity. In particular, we found that hippocampal neurons mostly project inhibitory connections toward the cortical counterpart modulating the temporal scale of the population events (network bursts). In contrast, cortical neurons establish a larger amount of intrapopulation connections. Moreover, we proved topological properties such as small-worldness, degree distribution, and modularity of neuronal assemblies were favored by the physical environment where networks developed and matured.

Relationships between gastric slow wave frequency, velocity, and extracellular amplitude studied by a joint experimental-theoretical approach

BACKGROUND

Gastric slow wave dysrhythmias are accompanied by deviations in frequency, velocity, and extracellular amplitude, but the inherent association between these parameters in normal activity still requires clarification. This study quantified these associations using a joint experimental-theoretical approach.

METHODS

Gastric pacing was conducted in pigs with simultaneous high-resolution slow wave mapping (32-256 electrodes; 4-7.6 mm spacing). Relationships between period, velocity, and amplitude were quantified and correlated for each wavefront. Human data from two existing mapping control cohorts were analyzed to extract and correlate these same parameters. A validated biophysically based ICC model was also applied in silico to quantify velocity-period relationships during entrainment simulations and velocity-amplitude relationships from membrane potential equations.

KEY RESULTS

Porcine pacing studies identified positive correlations for velocity-period (0.13 mm s^-1 per 1 s, r² =.63, P<.001) and amplitude-velocity (74 μV per 1 mm s^-1 , r² =.21, P=.002). In humans, positive correlations were also quantified for velocity-period (corpus: 0.11 mm s^-1 per 1 s, r² =.16, P<.001; antrum: 0.23 mm s^-1 per 1 s, r² =.55; P<.001), and amplitude-velocity (94 μV per 1 mm s^-1 , r² =.56; P<.001). Entrainment simulations matched the experimental velocity-period relationships and demonstrated dependence on the slow wave recovery phase. Simulated membrane potential relationships were close to these experimental results (100 μV per 1 mm s^-1 ).

CONCLUSIONS AND INFERENCES

These data quantify the relationships between slow wave frequency, velocity, and extracellular amplitude. The results from both human and porcine studies were in keeping with biophysical models, demonstrating concordance with ICC biophysics. These relationships are important in the regulation of gastric motility and will help to guide interpretations of dysrhythmias.

Wave Generation in Unidirectional Chains of Idealized Neural Oscillators

We investigate the dynamics of unidirectional semi-infinite chains of type-I oscillators that are periodically forced at their root node, as an archetype of wave generation in neural networks. In previous studies, numerical simulations based on uniform forcing have revealed that trajectories approach a traveling wave in the far-downstream, large time limit. While this phenomenon seems typical, it is hardly anticipated because the system does not exhibit any of the crucial properties employed in available proofs of existence of traveling waves in lattice dynamical systems. Here, we give a full mathematical proof of generation under uniform forcing in a simple piecewise affine setting for which the dynamics can be solved explicitly. In particular, our analysis proves existence, global stability, and robustness with respect to perturbations of the forcing, of families of waves with arbitrary period/wave number in some range, for every value of the parameters in the system.

Error correction and fast detectors implemented by ultrafast neuronal plasticity

We experimentally show that the neuron functions as a precise time integrator, where the accumulated changes in neuronal response latencies, under complex and random stimulation patterns, are solely a function of a global quantity, the average time lag between stimulations. In contrast, momentary leaps in the neuronal response latency follow trends of consecutive stimulations, indicating ultrafast neuronal plasticity. On a circuit level, this ultrafast neuronal plasticity phenomenon implements error-correction mechanisms and fast detectors for misplaced stimulations. Additionally, at moderate (high) stimulation rates this phenomenon destabilizes (stabilizes) a periodic neuronal activity disrupted by misplaced stimulations.

Rapid high-amplitude circumferential slow wave propagation during normal gastric pacemaking and dysrhythmias

BACKGROUND

Gastric slow waves propagate aborally as rings of excitation. Circumferential propagation does not normally occur, except at the pacemaker region. We hypothesized that (i) the unexplained high-velocity, high-amplitude activity associated with the pacemaker region is a consequence of circumferential propagation; (ii) rapid, high-amplitude circumferential propagation emerges during gastric dysrhythmias; (iii) the driving network conductance might switch between interstitial cells of Cajal myenteric plexus (ICC-MP) and circular interstitial cells of Cajal intramuscular (ICC-IM) during circumferential propagation; and (iv) extracellular amplitudes and velocities are correlated.

METHODS

An experimental-theoretical study was performed. High-resolution gastric mapping was performed in pigs during normal activation, pacing, and dysrhythmia. Activation profiles, velocities, and amplitudes were quantified. ICC pathways were theoretically evaluated in a bidomain model. Extracellular potentials were modeled as a function of membrane potentials.

KEY RESULTS

High-velocity, high-amplitude activation was only recorded in the pacemaker region when circumferential conduction occurred. Circumferential propagation accompanied dysrhythmia in 8/8 experiments was faster than longitudinal propagation (8.9 vs 6.9 mm s(-1) ; P = 0.004) and of higher amplitude (739 vs 528 μV; P = 0.007). Simulations predicted that ICC-MP could be the driving network during longitudinal propagation, whereas during ectopic pacemaking, ICC-IM could outpace and activate ICC-MP in the circumferential axis. Experimental and modeling data demonstrated a linear relationship between velocities and amplitudes (P < 0.001).

CONCLUSIONS & INFERENCES

The high-velocity and high-amplitude profile of the normal pacemaker region is due to localized circumferential propagation. Rapid circumferential propagation also emerges during a range of gastric dysrhythmias, elevating extracellular amplitudes and organizing transverse wavefronts. One possible explanation for these findings is bidirectional coupling between ICC-MP and circular ICC-IM networks.

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.

Designing Neural Networks in Culture: Experiments are described for controlled growth, of nerve cells taken from rats, in predesigned geometrical patterns on laboratory culture dishes

Technology has advanced to where it is possible to design and grow-with predefined geometry and surprisingly good fidelity-living networks of neurons in culture dishes. Here we overview the elements of design, emphasizing the lithographic techniques that alter the cell culture surface which in turn influences the attachment and growth of the neural networks. Advanced capability in this area makes it possible to design networks of desired complexity. Other issues addressed include the influence of glial cells and media on activity and the potential for extending the designs into three dimensions. Investigators are advancing the art and science of analyzing and controlling through stimulation the function of the neural networks, including the ability to take advantage of their geometric form in order to influence functional properties.

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.

Self-organization and neuronal avalanches in networks of dissociated cortical neurons

Dissociated cortical neurons from rat embryos cultured onto micro-electrode arrays exhibit characteristic patterns of electrophysiological activity, ranging from isolated spikes in the first days of development to highly synchronized bursts after 3-4 weeks in vitro. In this work we analyzed these features by considering the approach proposed by the self-organized criticality theory: we found that networks of dissociated cortical neurons also generate spontaneous events of spreading activity, previously observed in cortical slices, in the form of neuronal avalanches. Choosing an appropriate time scale of observation to detect such neuronal avalanches, we studied the dynamics by considering the spontaneous activity during acute recordings in mature cultures and following the development of the network. We observed different behaviors, i.e. sub-critical, critical or super-critical distributions of avalanche sizes and durations, depending on both the age and the development of cultures. In order to clarify this variability, neuronal avalanches were correlated with other statistical parameters describing the global activity of the network. Criticality was found in correspondence to medium synchronization among bursts and high ratio between bursting and spiking activity. Then, the action of specific drugs affecting global bursting dynamics (i.e. acetylcholine and bicuculline) was investigated to confirm the correlation between criticality and regulated balance between synchronization and variability in the bursting activity. Finally, a computational model of neuronal network was developed in order to interpret the experimental results and understand which parameters (e.g. connectivity, excitability) influence the distribution of avalanches. In summary, cortical neurons preserve their capability to self-organize in an effective network even when dissociated and cultured in vitro. The distribution of avalanche features seems to be critical in those cultures displaying medium synchronization among bursts and poor random spiking activity, as confirmed by chemical manipulation experiments and modeling studies.

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.