Modular Neuronal Network Research Articles

Two-Photon Polymerization 3D-Printing of Micro-scale Neuronal Cell Culture Devices.

Neuronal cultures have been a reference experimental model for several decades. However, 3D cell arrangement, spatial constraints on neurite outgrowth, and realistic synaptic connectivity are missing. The latter limits the study of structure and function in the context of compartmentalization and diminishes the significance of cultures in neuroscience. Approximating ex vivo the structured anatomical arrangement of synaptic connectivity is not trivial, despite being key for the emergence of rhythms, synaptic plasticity, and ultimately, brain pathophysiology. Here, two-photon polymerization (2PP) is employed as a 3D printing technique, enabling the rapid fabrication of polymeric cell culture devices using polydimethyl-siloxane (PDMS) at the micrometer scale. Compared to conventional replica molding techniques based on microphotolitography, 2PP micro-scale printing enables rapid and affordable turnaround of prototypes. This protocol illustrates the design and fabrication of PDMS-based microfluidic devices aimed at culturing modular neuronal networks. As a proof-of-principle, a two-chamber device is presented to physically constrain connectivity. Specifically, an asymmetric axonal outgrowth during ex vivo development is favored and allowed to be directed from one chamber to the other. In order to probe the functional consequences of unidirectional synaptic interactions, commercial microelectrode arrays are chosen to monitor the bioelectrical activity of interconnected neuronal modules. Here, methods to 1) fabricate molds with micrometer precision and 2) perform in vitro multisite extracellular recordings in rat cortical neuronal cultures are illustrated. By decreasing costs and future widespread accessibility of 2PP 3D-printing, this method will become more and more relevant across research labs worldwide. Especially in neurotechnology and high-throughput neural data recording, the ease and rapidity of prototyping simplified in vitro models will improve experimental control and theoretical understanding of in vivo large-scale neural systems.

Coherence resonance modulated by hybrid synapses and time delay in modular small-world neuronal networks with E–I balanced state

Coherence resonance modulated by hybrid synapses and time delay in modular small-world neuronal networks with E–I balanced state

Structure-function dynamics of engineered, modular neuronal networks with controllable afferent-efferent connectivity

Objective. Microfluidic devices interfaced with microelectrode arrays have in recent years emerged as powerful platforms for studying and manipulating in vitro neuronal networks at the micro- and mesoscale. By segregating neuronal populations using microchannels only permissible to axons, neuronal networks can be designed to mimic the highly organized, modular topology of neuronal assemblies in the brain. However, little is known about how the underlying topological features of such engineered neuronal networks contribute to their functional profile. To start addressing this question, a key parameter is control of afferent or efferent connectivity within the network. Approach. In this study, we show that a microfluidic device featuring axon guiding channels with geometrical constraints inspired by a Tesla valve effectively promotes unidirectional axonal outgrowth between neuronal nodes, thereby enabling us to control afferent connectivity. Main results. Our results moreover indicate that these networks exhibit a more efficient network organization with higher modularity compared to single nodal controls. We verified this by applying designer viral tools to fluorescently label the neurons to visualize the structure of the networks, combined with extracellular electrophysiological recordings using embedded nanoporous microelectrodes to study the functional dynamics of these networks during maturation. We furthermore show that electrical stimulations of the networks induce signals selectively transmitted in a feedforward fashion between the neuronal populations. Significance. A key advantage with our microdevice is the ability to longitudinally study and manipulate both the structure and function of neuronal networks with high accuracy. This model system has the potential to provide novel insights into the development, topological organization, and neuroplasticity mechanisms of neuronal assemblies at the micro- and mesoscale in healthy and perturbed conditions.

How synaptic plasticity affects the stochastic resonance in a modular neuronal network

How synaptic plasticity affects the stochastic resonance in a modular neuronal network

An in vitro model of neuronal ensembles

Advances in 3D neuronal cultures, such as brain spheroids and organoids, are allowing unprecedented in vitro access to some of the molecular, cellular and developmental mechanisms underlying brain diseases. However, their efficacy in recapitulating brain network properties that encode brain function remains limited, thereby precluding development of effective in vitro models of complex brain disorders like schizophrenia. Here, we develop and characterize a Modular Neuronal Network (MoNNet) approach that recapitulates specific features of neuronal ensemble dynamics, segregated local-global network activities and a hierarchical modular organization. We utilized MoNNets for quantitative in vitro modelling of schizophrenia-related network dysfunctions caused by highly penetrant mutations in SETD1A and 22q11.2 risk loci. Furthermore, we demonstrate its utility for drug discovery by performing pharmacological rescue of alterations in neuronal ensembles stability and global network synchrony. MoNNets allow in vitro modelling of brain diseases for investigating the underlying neuronal network mechanisms and systematic drug discovery.

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.

Spike signal transmission between modules and the predictability of spike activity in modular neuronal networks

Modularity is a common feature of the nervous system across species and scales. Although it has been qualitatively investigated in network science, very little is known about how it affects spike signal transmission in neuronal networks at the mesoscopic level. Here, a neuronal network model is built to simulate dynamic interactions among different modules of neuronal networks. This neuronal network model follows the organizational principle of modular structure. The neurons can generate spikes like biological neurons, and changes in the strength of synaptic connections conform to the STDP learning rule. Based on this neuronal network model, we first quantitatively studied whether and to what extent the connectivity within and between modules can affect spike signal transmission, and found that spike signal transmission heavily depends on the connectivity between modules, but has little to do with the connectivity within modules. More importantly, we further found that the spike activity of a module can be predicted according to the spike activities of its adjacent modules through building a resting-state functional connectivity matrix.

Less is more: wiring-economical modular networks support self-sustained firing-economical neural avalanches for efficient processing.

The brain network is notably cost-efficient, while the fundamental physical and dynamic mechanisms underlying its economical optimization in network structure and activity have not been determined. In this study, we investigate the intricate cost-efficient interplay between structure and dynamics in biologically plausible spatial modular neuronal network models. We observe that critical avalanche states from excitation-inhibition balance under modular network topology with less wiring cost can also achieve lower costs in firing but with strongly enhanced response sensitivity to stimuli. We derive mean-field equations that govern the macroscopic network dynamics through a novel approximate theory. The mechanism of low firing cost and stronger response in the form of critical avalanches is explained as a proximity to a Hopf bifurcation of the modules when increasing their connection density. Our work reveals the generic mechanism underlying the cost-efficient modular organization and critical dynamics widely observed in neural systems, providing insights into brain-inspired efficient computational designs.

Rhythmicity and firing modes in modular neuronal network under electromagnetic field

Based on a modified Hindmarsh–Rose model with electromagnetic induction being considered, rhythmicity and firing modes in modular neural network consisting of nonidentical neurons have been explored in detail. The global rhythmicity of the system shows a resonancelike behavior with the increase in the ratio of inactive neurons for strong coupling among neurons inside the subnetwork. We found that interaction between different subnetworks and electromagnetic induction parameter show the tendency to weaken dynamical robustness, whereas self-induction parameter could efficiently improve dynamical robustness of modular network. The dynamics of the active neuron on the road to aging transition is detected. The ratio of inactive neurons switches response-firing modes of the active neuron among spiking, periodic bursting and chaotic bursting. Our model system and results can provide new mechanism explanation for electrical activity in biological systems that are prone to suffer damage or deterioration.

Facilitating the propagation of spiking activity in feedforward networks by including feedback.

Transient oscillations in network activity upon sensory stimulation have been reported in different sensory areas of the brain. These evoked oscillations are the generic response of networks of excitatory and inhibitory neurons (EI-networks) to a transient external input. Recently, it has been shown that this resonance property of EI-networks can be exploited for communication in modular neuronal networks by enabling the transmission of sequences of synchronous spike volleys ('pulse packets'), despite the sparse and weak connectivity between the modules. The condition for successful transmission is that the pulse packet (PP) intervals match the period of the modules' resonance frequency. Hence, the mechanism was termed communication through resonance (CTR). This mechanism has three severe constraints, though. First, it needs periodic trains of PPs, whereas single PPs fail to propagate. Second, the inter-PP interval needs to match the network resonance. Third, transmission is very slow, because in each module, the network resonance needs to build up over multiple oscillation cycles. Here, we show that, by adding appropriate feedback connections to the network, the CTR mechanism can be improved and the aforementioned constraints relaxed. Specifically, we show that adding feedback connections between two upstream modules, called the resonance pair, in an otherwise feedforward modular network can support successful propagation of a single PP throughout the entire network. The key condition for successful transmission is that the sum of the forward and backward delays in the resonance pair matches the resonance frequency of the network modules. The transmission is much faster, by more than a factor of two, than in the original CTR mechanism. Moreover, it distinctly lowers the threshold for successful communication by synchronous spiking in modular networks of weakly coupled networks. Thus, our results suggest a new functional role of bidirectional connectivity for the communication in cortical area networks.

Robust prediction of complex spatiotemporal states through machine learning with sparse sensing

Complex spatiotemporal states arise frequently in material as well as biological systems consisting of multiple interacting units. A specific, but rather ubiquitous and interesting example is that of “chimeras”, existing in the edge between order and chaos. We use Machine Learning methods involving “observers” to predict the evolution of a system of coupled lasers, comprising turbulent chimera states and of a less chaotic biological one, of modular neuronal networks containing states that are synchronized across the networks. We demonstrated the necessity of using “observers” to improve the performance of Feed-Forward Networks in such complex systems. The robustness of the forecasting capabilities of the “Observer Feed-Forward Networks” versus the distribution of the observers, including equidistant and random, and the motion of them, including stationary and moving was also investigated. We conclude that the method has broader applicability in dynamical system context when partial dynamical information about the system is available.

Extended analysis of stochastic resonance in a modular neuronal network at different scales

Based on the firing dynamics at three different levels of microscale, mesoscale and macroscale, this study presents an extended analysis of stochastic resonance in a modular neuronal network in the spatially correlated white noise environment. Two well-defined modules of small-world subnetwork and scale-free subnetwork constitute the modular neuronal network in a hierarchical way. When a subthreshold periodic input is incorporated into this network, numerical results illustrate that a collective pattern of stochastic resonance emerges at macroscopic scale when the intensity of the correlated noise is appropriately tuned. Through extended analysis, one can detect that the firing rhythms of individual neurons gradually follow those of the periodic input at microscale. In addition, the occurrence of stochastic resonance at mesoscale in the small-world subnetwork is earlier than that in the scale-free subnetwork, and the peak height of resonance curve in the former subnetwork is remarkably higher than that in the latter one. These combined results indicate that the small-world subnetwork is more favorable than the scale-free subnetwork to induce stochastic resonance in this constructed modular network. The robustness of the extended analysis of stochastic resonance against variations in noise correlation coefficient and intra-module probability is also unveiled. This study provides a new perspective and tool to understand the collective phenomenon of stochastic resonance in realistic neuronal systems.

Suppressing bursting synchronization in a modular neuronal network with synaptic plasticity.

Excessive synchronization of neurons in cerebral cortex is believed to play a crucial role in the emergence of neuropsychological disorders such as Parkinson's disease, epilepsy and essential tremor. This study, by constructing a modular neuronal network with modified Oja's learning rule, explores how to eliminate the pathological synchronized rhythm of interacted busting neurons numerically. When all neurons in the modular neuronal network are strongly synchronous within a specific range of coupling strength, the result reveals that synaptic plasticity with large learning rate can suppress bursting synchronization effectively. For the relative small learning rate not capable of suppressing synchronization, the technique of nonlinear delayed feedback control including differential feedback control and direct feedback control is further proposed to reduce the synchronized bursting state of coupled neurons. It is demonstrated that the two kinds of nonlinear feedback control can eliminate bursting synchronization significantly when the control parameters of feedback strength and feedback delay are appropriately tuned. For the former control technique, the control domain of effective synchronization suppression is similar to a semi-elliptical domain in the simulated parameter space of feedback strength and feedback delay, while for the latter one, the effective control domain is similar to a fan-shaped domain in the simulated parameter space.

Autapse-induced multiple stochastic resonances in a modular neuronal network.

This study investigates the nontrivial effects of autapse on stochastic resonance in a modular neuronal network subjected to bounded noise. The resonance effect of autapse is detected by imposing a self-feedback loop with autaptic strength and autaptic time delay to each constituent neuron. Numerical simulations have demonstrated that bounded noise with the proper level of amplitude can induce stochastic resonance; moreover, the noise induced resonance dynamics can be significantly shaped by the autapse. In detail, for a specific range of autaptic strength, multiple stochastic resonances can be induced when the autaptic time delays are appropriately adjusted. These appropriately adjusted delays are detected to nearly approach integer multiples of the period of the external weak signal when the autaptic strength is very near zero; otherwise, they do not match the period of the external weak signal when the autaptic strength is slightly greater than zero. Surprisingly, in both cases, the differences between arbitrary two adjacent adjusted autaptic delays are always approximately equal to the period of the weak signal. The phenomenon of autaptic delay induced multiple stochastic resonances is further confirmed to be robust against the period of the external weak signal and the intramodule probability of subnetwork. These findings could have important implications for weak signal detection and information propagation in realistic neural systems.

The collective bursting dynamics in a modular neuronal network with synaptic plasticity

In this study, how the synaptic plasticity influences the collective bursting dynamics in a modular neuronal network is numerically investigated. The synaptic plasticity is described by a modified Oja’s learning rule. The modular network is composed of some sub-networks, each of them having small-world characteristic. The result indicates that bursting synchronization can be induced by large coupling strength between different neurons, which is robust to the local dynamical parameter of individual neurons. With the emergence of synaptic plasticity, the bursting dynamics in the modular neuronal network, particularly the excitability and synchronizability of bursting neurons, is detected to be changed significantly. In detail, upon increasing synaptic learning rate, the excitability of bursting neurons is greatly enhanced; on the contrary, bursting synchronization between interacted neurons is a little suppressed by the increase in synaptic learning rate. The presented findings could be helpful to understand the important role of synaptic plasticity on neural coding in realistic neuronal network.

Partial coupling delay induced multiple spatiotemporal orders in a modular neuronal network.

The influence of partial coupling delay on the spatiotemporal spiking dynamics is explored in a modular neuronal network. The modular neuronal network is composed of two subnetworks which present the small-world property and scale-free property, respectively. Numerical results show that spatiotemporal order that the modular network is most coherent in time and nearly synchronized in space can emerge intermittently when the coupling delays among neurons are appropriately tuned. The appropriately tuned delays are further detected to be integer multiples of the intrinsic spiking period of the modular neuronal network, which implies that the phenomenon of multiple spatiotemporal orders could be the result of a locking between the length of coupling delay and the intrinsic spiking period of the modular neuronal network. Moreover, the multiple spatiotemporal orders are verified to be robust against variations of the fraction of delayed connection as well as the key parameters of network architecture such as the rewiring probability, the average degree of small-world subnetwork, the initial nodes of scale-free subnetwork and the total size of the modular network.

How time-delayed coupling influences differential feedback control of bursting synchronization in modular neuronal network

The nontrivial influence of time-delayed coupling on differential feedback control of bursting synchronization is explored in modular neuronal network. Numerical simulations show that collective rhythm of bursting synchronization, irrespective of the numbers of subnetworks, can appear when the considered modular network is forced by large coupling. Then, a control domain of effective synchronization suppression is detected when the proposed differential feedback control is applied to suppress bursting synchronization. Furthermore, time delay in the coupling is introduced, and how it affects differential feedback control to inhibit bursting synchronization is explored. The result declares that small time delay can enhance differential feedback control to suppress bursting synchronization, and there exists an optimal time delay such that this enhancement can obtain its maximum. This presented result is expected to facilitate us to suppress bursting synchronization in realistic neuronal networks.

The evolution to global burst synchronization in a modular neuronal network

In this paper, we investigated the development of global burst synchronization in a modular neuronal network at the mesoscale level. The modular network consists of some subnetworks, each of them presenting a scale-free property. Numerical results have demonstrated that, upon increasing the coupling strength, all neurons in the modular network initially burst in a desynchronous pattern; then the burst synchronization within each subnetwork is followed at the mesoscale; finally, the global burst synchronization at the macroscale is formed by the bursting activities on each subnetwork moving forward in harmony. This implies the network behavior possesses two distinct mesoscopic and macroscopic properties for some coupling strengths, i.e. the mesoscopic dynamics of burst synchronization on subnetworks is different from the macroscopic property of desynchronous activity on the whole network. It is also found that global burst synchronization can be promoted by large interconnection probability and hindered by small interconnection probability.

Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits

The brain operates through the coordinated activation and the dynamic communication of neuronal assemblies. A major open question is how a vast repertoire of dynamical motifs, which underlie most diverse brain functions, can emerge out of a fixed topological and modular organization of brain circuits. Compared to in vivo studies of neuronal circuits which present intrinsic experimental difficulties, in vitro preparations offer a much larger possibility to manipulate and probe the structural, dynamical and chemical properties of experimental neuronal systems. This work describes an in vitro experimental methodology which allows growing of modular networks composed by spatially distinct, functionally interconnected neuronal assemblies. The protocol allows controlling the two-dimensional (2D) architecture of the neuronal network at different levels of topological complexity. A desired network patterning can be achieved both on regular cover slips and substrate embedded micro electrode arrays. Micromachined structures are embossed on a silicon wafer and used to create biocompatible polymeric stencils, which incorporate the negative features of the desired network architecture. The stencils are placed on the culturing substrates during the surface coating procedure with a molecular layer for promoting cellular adhesion. After removal of the stencils, neurons are plated and they spontaneously redirected to the coated areas. By decreasing the inter-compartment distance, it is possible to obtain either isolated or interconnected neuronal circuits. To promote cell survival, cells are co-cultured with a supporting neuronal network which is located at the periphery of the culture dish. Electrophysiological and optical recordings of the activity of modular networks obtained respectively by using substrate embedded micro electrode arrays and calcium imaging are presented. While each module shows spontaneous global synchronizations, the occurrence of inter-module synchronization is regulated by the density of connection among the circuits.

Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits

The brain operates through the coordinated activation and the dynamic communication of neuronal assemblies. A major open question is how a vast repertoire of dynamical motifs, which underlie most diverse brain functions, can emerge out of a fixed topological and modular organization of brain circuits. Compared to in vivo studies of neuronal circuits which present intrinsic experimental difficulties, in vitro preparations offer a much larger possibility to manipulate and probe the structural, dynamical and chemical properties of experimental neuronal systems. This work describes an in vitro experimental methodology which allows growing of modular networks composed by spatially distinct, functionally interconnected neuronal assemblies. The protocol allows controlling the two-dimensional (2D) architecture of the neuronal network at different levels of topological complexity. A desired network patterning can be achieved both on regular cover slips and substrate embedded micro electrode arrays. Micromachined structures are embossed on a silicon wafer and used to create biocompatible polymeric stencils, which incorporate the negative features of the desired network architecture. The stencils are placed on the culturing substrates during the surface coating procedure with a molecular layer for promoting cellular adhesion. After removal of the stencils, neurons are plated and they spontaneously redirected to the coated areas. By decreasing the inter-compartment distance, it is possible to obtain either isolated or interconnected neuronal circuits. To promote cell survival, cells are co-cultured with a supporting neuronal network which is located at the periphery of the culture dish. Electrophysiological and optical recordings of the activity of modular networks obtained respectively by using substrate embedded micro electrode arrays and calcium imaging are presented. While each module shows spontaneous global synchronizations, the occurrence of inter-module synchronization is regulated by the density of connection among the circuits.