Singing of <Emphasis Type="Italic">Neoconocephalus robustus</Emphasis> as an example of deterministic chaos in insects

We use nonlinear time series analysis methods to analyse the dynamics of the sound-producing apparatus of the katydid Neoconocephalus robustus. We capture the dynamics by analysing a recording of the singing activity. First, we reconstruct the phase space from the sound recording and test it against determinism and stationarity. After confirming determinism and stationarity, we show that the maximal Lyapunov exponent of the series is positive, which is a strong indicator for the chaotic behaviour of the system. We discuss that methods of nonlinear time series analysis can yield instructive insights and foster the understanding of acoustic communication among insects.     

Single-chip microelectronic system to interface with living cells

A high degree of connectivity and the coordinated electrical activity of neural cells or networks are believed to be the reason that the brain is capable of highly sophisticated information processing. Likewise, the effectiveness of an animal heart largely depends on such coordinated cell activity. To advance our understanding of these complex biological systems, high spatiotemporal-resolution techniques to monitor the cell electrical activity and an ideally seamless interaction between cells and recording devices are desired. Here we present a monolithic microsystem in complementary metal oxide semiconductor (CMOS) technology that provides bidirectional communication (stimulation and recording) between standard electronics technology and cultured electrogenic cells. The microchip can be directly used as a substrate for cell culturing, it features circuitry units per electrode for stimulation and immediate cell signal treatment, and it provides on-chip signal transformation as well as a digital interface so that a very fast, almost real-time interaction (2 ms loop time from event recognition to, e.g., a defined stimulation) is possible at remarkable signal quality. The corresponding spontaneous and stimulated electrical activity recordings with neuronal and cardiac cell cultures will be presented. The system can be used to, e.g., study the development of neural networks, reveal the effects of neuronal plasticity and study cellular or network activity in response to pharmacological treatments.     

Nonlinearities in mating sounds of American crocodiles

We use nonlinear time series analysis methods to analyze the dynamics of the sound-producing apparatus of the American crocodile (Crocodylus acutus). We capture its dynamics by analyzing a recording of the singing activity during mating time. First, we reconstruct the phase space from the sound recording and thereby reveal that the attractor needs no less than five degrees of freedom to fully evolve in the embedding space, which suggests that a rather complex nonlinear dynamics underlies its existence. Prior to investigating the dynamics more precisely, we test whether the reconstructed attractor satisfies the notions of determinism and stationarity, as a lack of either of these properties would preclude a meaningful further analysis. After positively establishing determinism and stationarity, we proceed by showing that the maximal Lyapunov exponent of the recording is positive, which is a strong indicator for the chaotic behavior of the system, confirming that dynamical nonlinearities are an integral part of the examined sound-producing apparatus. At the end, we discuss that methods of nonlinear time series analysis could yield instructive insights and foster the understanding of vocal communication among certain reptile species.     

Congruent qualitative behavior of complete and reconstructed phase space trajectories from biomolecular dynamics simulation

Central to the study of a complex dynamical system is knowledge of its phase space behavior. Experimentally, it is rarely possible to record a system's (multidimensional) phase space variables. Rather, the system is observed via one (or few) scalar-valued signal(s) of emission or response. In dynamical systems analysis, the multidimensional phase space of a system can be reconstructed by manipulation of a one-dimensional signal. The trick is in the construction of a (higher-dimensional) space through the use of a time lag (or delay) on the signal time series. The trajectory in this embedding space can then be examined using phase portraits generated in selected subspaces. By contrast, in computer simulation, one has an embarrassment of riches: direct access to the complete multidimensional phase space variables, at arbitrary time resolution and precision. Here, the problem is one of reducing the dimensionality to make analysis tractable. This can be achieved through linear or nonlinear projection of the trajectory into subspaces containing high information content. This study considers trajectories of the small protein crambin from molecular dynamics simulations. The phase space behavior is examined using principal component analysis on the Cartesian coordinate covariance matrix of 138 dimensions. In addition, the phase space is reconstructed from a one dimensional signal, representing the radius of gyration of the structure along the trajectory. Comparison of low-dimensional phase portraits obtained from the two methods shows that the complete phase space distribution is well represented by the reconstruction. The study suggests that it may be possible to develop a deeper connection between the experimental and simulated dynamics of biomolecules via phase space reconstruction using data emerging from recent advances in single-molecule time-resolved biophysical techniques.     

A portable microelectrode array recording system incorporating cultured neuronal networks for neurotoxin detection

Cultured neuronal networks, which have the capacity to respond to a wide range of neuroactive compounds, have been suggested to be useful for both screening known analytes and unknown compounds for acute neuropharmacologic effects. Extracellular recording from cultured neuronal networks provides a means for extracting physiologically relevant activity, i.e. action potential firing, in a noninvasive manner conducive for long-term measurements. Previous work from our laboratory described prototype portable systems capable of high signal-to-noise extracellular recordings from cardiac myocytes. The present work describes a portable system tailored to monitoring neuronal extracellular potentials that readily incorporates standardized microelectrode arrays developed by and in use at the University of North Texas. This system utilizes low noise amplifier and filter boards, a two-stage thermal control system with integrated fluidics and a graphical user interface for data acquisition and control implemented on a personal computer. Wherever possible, off-the-shelf components have been utilized for system design and fabrication. During use with cultured neuronal networks, the system typically exhibits input referred noise levels of only 4-6 microVRMS, such that extracellular potentials exceeding 40 microV can be readily resolved. A flow rate of up to 1 ml/min was achieved while the cell recording chamber temperature was maintained within a range of 36-37 degrees C. To demonstrate the capability of this system to resolve small extracellular potentials, pharmacological experiments with cultured neuronal networks have been performed using ion channel blockers, tetrodotoxin and tityustoxin. The implications of the experiments for neurotoxin detection are discussed.     

Large-Scale,High-Resolution Multielectrode-Array Recording Depicts Functional Network Differences of Cortical and Hippocampal Cultures

Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30–80 Hz) and beta (12–30 Hz) range) showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100–1000 Hz). The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.     

Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation

In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural assemblies and behavioural patterns, the linkage between them, and their modifications over time, cannot be fully understood in the context of even integrative physiology, without using these new techniques. This report, which is the first of two related papers, is aimed at introducing the non expert to the fundamental aspects of nonlinear dynamics, the most spectacular aspect of which is chaos theory. After a general history and definition of chaos the principles of analysis of time series in phase space and the general properties of chaotic trajectories will be described as will be the classical measures which allow a process to be classified as chaotic in ideal systems and models. We will then proceed to show how these methods need to be adapted for handling experimental time series; the dangers and pitfalls faced when dealing with non stationary and often noisy data will be stressed, and specific criteria for suspecting determinism in neuronal cells and/or assemblies will be described. We will finally address two fundamental questions, namely i) whether and how can one distinguish, deterministic patterns from stochastic ones, and, ii) what is the advantage of chaos over randomness: we will explain why and how the former can be controlled whereas, notoriously, the latter cannot be tamed. In the second paper of the series, results obtained at the level of single cells and their membrane conductances in real neuronal networks and in the study of higher brain functions, will be critically reviewed. It will be shown that the tools of nonlinear dynamics can be irreplaceable for revealing hidden mechanisms subserving, for example, neuronal synchronization and periodic oscillations. The benefits for the brain of adopting chaotic regimes with their wide range of potential behaviours and their aptitude to quickly react to changing conditions will also be considered.     

Validation of long-term primary neuronal cultures and network activity through the integration of reversibly bonded microbioreactors and MEA substrates

In vitro recording of neuronal electrical activity is a widely used technique to understand brain functions and to study the effect of drugs on the central nervous system. The integration of microfluidic devices with microelectrode arrays (MEAs) enables the recording of networks activity in a controlled microenvironment. In this work, an integrated microfluidic system for neuronal cultures was developed, reversibly coupling a PDMS microfluidic device with a commercial flat MEA through magnetic forces. Neurons from mouse embryos were cultured in a 100 μm channel and their activity was followed up to 18 days in vitro. The maturation of the networks and their morphological and functional characteristics were comparable with those of networks cultured in macro-environments and described in literature. In this work, we successfully demonstrated the ability of long-term culturing of primary neuronal cells in a reversible bonded microfluidic device (based on magnetism) that will be fundamental for neuropharmacological studies.     

Studying the mechanisms of genomic and synaptic plasticity in neuronal cultures with microelectrode arrays

The plasticity of neural networks is a complex process determined by changes in physiological status, gene expression and phenotype of a cell. A detailed study of this process dynamics requires the simultaneous recording of electrical and genomic activities in networks of neurons. This sets up one of the tasks for modern neuroscience as development of integration of electrophysiology and molecular biology methods. In the paper we review the current approaches to such integration, as well as the choice of molecular markers for detection of genomic and synaptic plasticity of neurons by use of physiological micro-sensorial system based on neuronal cells cultured on the micro-electrode arrays.     

Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales

Recent studies have emphasized the importance of multiplex networks – interdependent networks with shared nodes and different types of connections – in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy – an information theoretic quantity that can be used to measure linear and nonlinear interactions – to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons (“hubs”) were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.     

On the synthesis of DNA error correcting codes

Regeneration of damaged central nervous systems (CNS) is an important topic in neuroscience and neuroengineering. Grafting new neurons derived from pluripotent stem cells into damaged regions can be done to restore functions after injury. Little is known, however, about network-wide interactions between stem-cell-derived neurons and CNS neurons. In this study, we developed a co-culture method of stem cell-derived neuronal networks and CNS networks and observed spontaneous activity in the co-culture samples. By using a microfabricated poly(dimethylsiloxane) device having two culture compartments and 20 connecting microconduits, we are able to compartmentalize P19-derived neurons and mouse cortical neurons and connect them via the microconduits. Furthermore, we combined the co-culture device and a microelectrode array (MEA)-based recording system and recorded spontaneous activity in the co-cultured networks. We found that periodic synchronized bursting spreading over both neuronal networks occurred during the second week in vitro and that P19-derived neurons in the co-cultured networks had different developmental processes compared with those grown in monoculture. These findings suggest that functional interactions form between P19-dervived neurons and mouse cortical neurons and that the co-culture method is useful for exploring the network-wide integrations between stem cell-derived neurons and CNS neurons.     

Functional organization and structure of the serotonergic neuronal network of terrestrial snail

The extension of knowledge how the brain works requires permanent improvement of methods of recording of neuronal activity and increase in the number of neurons recorded simultaneously to better understand the collective work of neuronal networks and assemblies. Conventional methods allow simultaneous intracellular recording up to 2-5 neurons and their membrane potentials, currents or monosynaptic connections or observation of spiking of neuronal groups with subsequent discrimination of individual spikes with loss of details of the dynamics of membrane potential. We recorded activity of a compact group of serotonergic neurons (up to 56 simultaneously) in the ganglion of a terrestrial mollusk using the method of optical recording of membrane potential that allowed to record individual action potentials in details with action potential parameters and to reveal morphology of the neurons rcorded. We demonstrated clear clustering in the group in relation with the dynamics of action potentials and phasic or tonic components in the neuronal responses to external electrophysiological and tactile stimuli. Also, we showed that identified neuron Pd2 could induce activation of a significant number of neurons in the group whereas neuron Pd4 did not induce any activation. However, its activation is delayed with regard to activation of the reacting group of neurons. Our data strongly support the concept of possible delegation of the integrative function by the network to a single neuron.     

Searching for optimal stimuli: ascending a neuron’s response function

Many methods used to analyze neuronal response assume that neuronal activity has a fundamentally linear relationship to the stimulus. However, some neurons are strongly sensitive to multiple directions in stimulus space and have a highly nonlinear response. It can be difficult to find optimal stimuli for these neurons. We demonstrate how successive linear approximations of neuronal response can effectively carry out gradient ascent and move through stimulus space towards local maxima of the response. We demonstrate search results for a simple model neuron and two models of a highly selective neuron.     

An image-free opto-mechanical system for creating virtual environments and imaging neuronal activity in freely moving Caenorhabditis elegans

Non-invasive recording in untethered animals is arguably the ultimate step in the analysis of neuronal function, but such recordings remain elusive. To address this problem, we devised a system that tracks neuron-sized fluorescent targets in real time. The system can be used to create virtual environments by optogenetic activation of sensory neurons, or to image activity in identified neurons at high magnification. By recording activity in neurons of freely moving C. elegans, we tested the long-standing hypothesis that forward and reverse locomotion are generated by distinct neuronal circuits. Surprisingly, we found motor neurons that are active during both types of locomotion, suggesting a new model of locomotion control in C. elegans. These results emphasize the importance of recording neuronal activity in freely moving animals and significantly expand the potential of imaging techniques by providing a mean to stabilize fluorescent targets.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Study on the transient characteristic in the human visual system using masking experiments

In this paper the visual masking effect is interpreted on the basis of the transient characteristic in two dimensional neuronal networks. The study investigates the suitability of the effect for use as a measurement method. It is shown that the stimulus distribution in space can be scanned at different points in time and that various dynamic characteristic values of the system can be measured.This paper was supported by the DFG with grant no. Se 251/13; Prof. W. von Seelen was in charge of the project     

Frequency Control in Synchronized Networks of Inhibitory Neurons

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called phasic, is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.