Growth of cortical neuronal network in vitro: modeling and analysis

Optimized two-dimensional networks with edge-crossing cost: Frustrated antiferromagnetic spin system

We consider a quasi-two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute antiferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean-field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

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

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

Neural electrical activity and neural network growth

The development of central and peripheral neural system depends in part on the emergence of the correct functional connectivity in its input and output pathways. Now it is generally accepted that molecular factors guide neurons to establish a primary scaffold that undergoes activity-dependent refinement for building a fully functional circuit. However, a number of experimental results obtained recently shows that the neuronal electrical activity plays an important role in the establishing of initial interneuronal connections. Nevertheless, these processes are rather difficult to study experimentally, due to the absence of theoretical description and quantitative parameters for estimation of the neuronal activity influence on growth in neural networks. In this work we propose a general framework for a theoretical description of the activity-dependent neural network growth. The theoretical description incorporates a closed-loop growth model in which the neural activity can affect neurite outgrowth, which in turn can affect neural activity. We carried out the detailed quantitative analysis of spatiotemporal activity patterns and studied the relationship between individual cells and the network as a whole to explore the relationship between developing connectivity and activity patterns. The model, developed in this work will allow us to develop new experimental techniques for studying and quantifying the influence of the neuronal activity on growth processes in neural networks and may lead to a novel techniques for constructing large-scale neural networks by self-organization.

Simulation of developing human neuronal cell networks

Background

Microelectrode array (MEA) is a widely used technique to study for example the functional properties of neuronal networks derived from human embryonic stem cells (hESC-NN). With hESC-NN, we can investigate the earliest developmental stages of neuronal network formation in the human brain.

Methods

In this paper, we propose an in silico model of maturating hESC-NNs based on a phenomenological model called INEX. We focus on simulations of the development of bursts in hESC-NNs, which are the main feature of neuronal activation patterns. The model was developed with data from developing hESC-NN recordings on MEAs which showed increase in the neuronal activity during the investigated six measurement time points in the experimental and simulated data.

Results

Our simulations suggest that the maturation process of hESC-NN, resulting in the formation of bursts, can be explained by the development of synapses. Moreover, spike and burst rate both decreased at the last measurement time point suggesting a pruning of synapses as the weak ones are removed.

Conclusions

To conclude, our model reflects the assumption that the interaction between excitatory and inhibitory neurons during the maturation of a neuronal network and the spontaneous emergence of bursts are due to increased connectivity caused by the forming of new synapses.

Effects of simulated microgravity on human brain nervous tissue

During spaceflight, the negative effects of space microgravity on astronauts are becoming more and more prominent, and especially, of which on the nervous system is urgently to be solved. For this purpose tissue blocks and primary cells of nervous tissues obtained from glioma of patients were cultivated after culturing for about 7days, explanted tissues and cells were then randomly divided into two groups, one for static culture (control group, C), and the other for rotary processing for 1day, 3days, 5days, 7days and 14days (experiment group, E). Figures captured by inverted microscope revealed that, with short time rotating for 1day or 3days, morphology changes of tissue blocks were not obvious. When the rotary time was extended to 7days or 14days, it was found that cell somas is significantly larger and the ability of adhesion is declined in comparison with that in control group. Additionally, the arrangement of cells migrated from explanted tissues was disorganized, and the migration distance became shorter. In immunofluorescence analysis, β-tubulin filaments in control group appeared to organize into bundles. While in experiment group, β-tubulin was highly disorganized. In conclusion, simulated microgravity treatment for a week affected the morphology of nervous tissue, and caused highly disorganized distribution of cytoskeleton and the increase of cell apoptosis. These morphological changes might be one of the causes of apoptosis induced by simulated microgravity.

Combined Exposure to Simulated Microgravity and Acute or Chronic Radiation Reduces Neuronal Network Integrity and Survival

During orbital or interplanetary space flights, astronauts are exposed to cosmic radiations and microgravity. However, most earth-based studies on the potential health risks of space conditions have investigated the effects of these two conditions separately. This study aimed at assessing the combined effect of radiation exposure and microgravity on neuronal morphology and survival in vitro. In particular, we investigated the effects of simulated microgravity after acute (X-rays) or during chronic (Californium-252) exposure to ionizing radiation using mouse mature neuron cultures. Acute exposure to low (0.1 Gy) doses of X-rays caused a delay in neurite outgrowth and a reduction in soma size, while only the high dose impaired neuronal survival. Of interest, the strongest effect on neuronal morphology and survival was evident in cells exposed to microgravity and in particular in cells exposed to both microgravity and radiation. Removal of neurons from simulated microgravity for a period of 24 h was not sufficient to recover neurite length, whereas the soma size showed a clear re-adaptation to normal ground conditions. Genome-wide gene expression analysis confirmed a modulation of genes involved in neurite extension, cell survival and synaptic communication, suggesting that these changes might be responsible for the observed morphological effects. In general, the observed synergistic changes in neuronal network integrity and cell survival induced by simulated space conditions might help to better evaluate the astronaut's health risks and underline the importance of investigating the central nervous system and long-term cognition during and after a space flight.

Reconstruction of network structures from repeating spike patterns in simulated bursting dynamics

Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies (from random to scale free) have been simulated to study the effectiveness of the pattern-matching method in the reconstruction of network topology from network dynamics. Simulation results show that functional networks reconstructed from repeating spike patterns can be quite different from the original physical networks; even global properties, such as the degree distribution, cannot always be recovered. However, the pattern-matching method can be effective in identifying hubs in the network. Since the form of reverberations is quite different for networks with and without hubs, the form of reverberations together with the reconstruction by repeating spike patterns might provide a reliable method to detect hubs in neuronal cultures.

MorphoNeuroNet: an automated method for dense neurite network analysis

High content cell-based screens are rapidly gaining popularity in the context of neuronal regeneration studies. To analyze neuronal morphology, automatic image analysis pipelines have been conceived, which accurately quantify the shape changes of neurons in cell cultures with non-dense neurite networks. However, most existing methods show poor performance for well-connected and differentiated neuronal networks, which may serve as valuable models for inter alia synaptogenesis. Here, we present a fully automated method for quantifying the morphology of neurons and the density of neurite networks, in dense neuronal cultures, which are grown for more than 10 days. MorphoNeuroNet, written as a script for ImageJ, Java based freeware, automatically determines various morphological parameters of the soma and the neurites (size, shape, starting points, and fractional occupation). The image analysis pipeline consists of a multi-tier approach in which the somas are segmented by adaptive region growing using nuclei as seeds, and the neurites are delineated by a combination of various intensity and edge detection algorithms. Quantitative comparison showed a superior performance of MorphoNeuroNet to existing analysis tools, especially for revealing subtle changes in thin neurites, which have weak fluorescence intensity compared to the rest of the network. The proposed method will help determining the effects of compounds on cultures with dense neurite networks, thereby boosting physiological relevance of cell-based assays in the context of neuronal diseases.

Morphological and physiological changes in mature in vitro neuronal networks towards exposure to short-, middle- or long-term simulated microgravity

One of the objectives of the current international space programmes is to investigate the possible effects of the space environment on the crew health. The aim of this work was to assess the particular effects of simulated microgravity on mature primary neuronal networks and specially their plasticity and connectivity. For this purpose, primary mouse neurons were first grown for 10 days as a dense network before being placed in the Random Positioning Machine (RPM), simulating microgravity. These cultures were then used to investigate the impact of short- (1 h), middle- (24 h) and long-term (10 days) exposure to microgravity at the level of neurite network density, cell morphology and motility as well as cytoskeleton properties in established two-dimensional mature neuronal networks. Image processing analysis of dense neuronal networks exposed to simulated microgravity and their subsequent recovery under ground conditions revealed different neuronal responses depending on the duration period of exposure. After short- and middle-term exposures to simulated microgravity, changes in neurite network, neuron morphology and viability were observed with significant alterations followed by fast recovery processes. Long exposure to simulated microgravity revealed a high adaptation of single neurons to the new gravity conditions as well as a partial adaptation of neuronal networks. This latter was concomitant to an increase of apoptosis. However, neurons and neuronal networks exposed for long-term to simulated microgravity required longer recovery time to re-adapt to the ground gravity. In conclusion, a clear modulation in neuronal plasticity was evidenced through morphological and physiological changes in primary neuronal cultures during and after simulated microgravity exposure. These changes were dependent on the duration of exposure to microgravity.

Event-driven simulations of a plastic, spiking neural network

We consider a fully connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing randomly with the same mean frequency. For low values of the plasticity parameter, the activities of the system are dominated by noise, while large values of the plasticity parameter lead to self-sustaining activity in the network. We perform event-driven simulations on finite-size networks with up to 128 neurons to find the stationary synaptic weight conformations for different values of the plasticity parameter. In both the low- and high-activity regimes, the synaptic weights are narrowly distributed around the plasticity parameter value consistent with the predictions of mean-field theory. However, the distribution broadens in the transition region between the two regimes, representing emergent network structures. Using a pseudophysical approach for visualization, we show that the emergent structures are of "path" or "hub" type, observed at different values of the plasticity parameter in the transition region.

Effects of glial release and somatic receptors on bursting in synchronized neuronal networks

A model is constructed to study the phenomenon of bursting in cultured neuronal networks by considering the effects of glial release and the extrasynaptic receptors on neurons. In the frequently observed situations of synchronized bursting, the whole neuronal network can be described by a mean-field model. In this model, the dynamics of the synchronized network in the presence of glia is represented by an effective two-compartment neuron with stimulations on both the dendrite and soma. Numerical simulations of this model show that most of the experimental observations in bursting, in particular the high plateau and the slow repolarization, can be reproduced. Our findings suggest that the effects of glia release and extrasynaptic receptors, which are usually neglected in neuronal models, can become important in intense network activities. Furthermore, simulations of the model are also performed for the case of glia-suppressed cultures to compare with recent experimental results.

Frequency enhancement in coupled noisy excitable elements

Oscillatory dynamics of coupled excitable FitzHugh-Nagumo elements in the presence of noise is investigated as a function of the coupling strength g. For two such coupled elements, their frequencies are enhanced and will synchronize at a frequency higher than the uncoupled frequencies of each element. As g increases, there is an unexpected peak in the frequency enhancement before reaching synchronization. The results can be understood with an analytic model based on the excitation across a potential barrier whose height is controlled by g. Simulation results of a coupled square lattice can quantitatively reproduce the unexpected peak in the variation of the beating rates observed in cultured cardiac cells experiments.

Mean-field theory of a plastic network of integrate-and-fire neurons

We consider a noise-driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity. Assuming Poisson firing statistics for the neurons, the plasticity dynamics of a synapse under the influence of the mean-field environment can be mapped to the dynamics of an asymmetric random walk in synaptic-weight space. Using a master equation for small steps, we predict a narrow distribution of synaptic weights that scales with the square root of the plasticity rate for the stationary state of the system given plausible physiological parameter values describing neural transmission and plasticity. The dependence of the distribution on the synaptic weight of the mean-field environment allows us to determine the mean synaptic weight self-consistently. The effect of fluctuations in the total synaptic conductance and plasticity step sizes are also considered. Such fluctuations result in a smoothing of the first-order transition for low number of afferent synapses per neuron and a broadening of the synaptic-weight distribution, respectively.