Synaptic efficacy and the transmission of complex firing patterns between neurons

Hyperpolarization-Activated Current Induces Period-Doubling Cascades and Chaos in a Cold Thermoreceptor Model

In this article, we describe and analyze the chaotic behavior of a conductance-based neuronal bursting model. This is a model with a reduced number of variables, yet it retains biophysical plausibility. Inspired by the activity of cold thermoreceptors, the model contains a persistent Sodium current, a Calcium-activated Potassium current and a hyperpolarization-activated current (I_h) that drive a slow subthreshold oscillation. Driven by this oscillation, a fast subsystem (fast Sodium and Potassium currents) fires action potentials in a periodic fashion. Depending on the parameters, this model can generate a variety of firing patterns that includes bursting, regular tonic and polymodal firing. Here we show that the transitions between different firing patterns are often accompanied by a range of chaotic firing, as suggested by an irregular, non-periodic firing pattern. To confirm this, we measure the maximum Lyapunov exponent of the voltage trajectories, and the Lyapunov exponent and Lempel-Ziv's complexity of the ISI time series. The four-variable slow system (without spiking) also generates chaotic behavior, and bifurcation analysis shows that this is often originated by period doubling cascades. Either with or without spikes, chaos is no longer generated when the I_h is removed from the system. As the model is biologically plausible with biophysically meaningful parameters, we propose it as a useful tool to understand chaotic dynamics in neurons.

Synaptic variability in a cortical neuromorphic circuit

Variable behavior has been observed in several mechanisms found in biological neurons, resulting in changes in neural behavior that might be useful to capture in neuromorphic circuits. This paper presents a neuromorphic cortical neuron with synaptic neurotransmitter-release variability, which is designed to be used in neural networks as part of the Biomimetic Real-Time Cortex project. This neuron has been designed and simulated using carbon nanotube (CNT) transistors, which is one of several nanotechnologies under consideration to meet the challenges of scale presented by the cortex. Some research results suggest that some instances of variability are stochastic, while others indicate that some instances of variability are chaotic. In this paper, both possible sources of variability are considered by embedding either Gaussian noise or a chaotic signal into the neuromorphic or synaptic circuit and observing the simulation results. In order to embed chaotic behavior into the neuromorphic circuit, a chaotic signal generator circuit is presented, implemented with CNT transistors that could be embedded in the electronic neural circuit, and simulated using CNT SPICE models. The circuit uses a chaotic piecewise linear 1-D map implemented by switched-current circuits. The simulation results presented in this paper illustrate that neurotransmitter-release variability plays a beneficial role in the reliability of spike generation. In an examination of this reliability, the precision of spike timing in the CNT circuit simulations is found to be dependent on stimulus (postsynaptic potential) transients. Postsynaptic potentials with low neurotransmitter release variability or without neurotransmitter release variability produce imprecise spike trains, whereas postsynaptic potentials with high neurotransmitter-release variability produce spike trains with reproducible timing.

Noise destroys feedback enhanced figure-ground segmentation but not feedforward figure-ground segmentation

Figure-ground (FG) segmentation is the separation of visual information into background and foreground objects. In the visual cortex, FG responses are observed in the late stimulus response period, when neurons fire in tonic mode, and are accompanied by a switch in cortical state. When such a switch does not occur, FG segmentation fails. Currently, it is not known what happens in the brain on such occasions. A biologically plausible feedforward spiking neuron model was previously devised that performed FG segmentation successfully. After incorporating feedback the FG signal was enhanced, which was accompanied by a change in spiking regime. In a feedforward model neurons respond in a bursting mode whereas in the feedback model neurons fired in tonic mode. It is known that bursts can overcome noise, while tonic firing appears to be much more sensitive to noise. In the present study, we try to elucidate how the presence of noise can impair FG segmentation, and to what extent the feedforward and feedback pathways can overcome noise. We show that noise specifically destroys the feedback enhanced FG segmentation and leaves the feedforward FG segmentation largely intact. Our results predict that noise produces failure in FG perception.

Noise in the nervous system

Noise--random disturbances of signals--poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.

Stem cell growth becomes predominant while neural plate progenitor pool decreases during spinal cord elongation

The antero-posterior dispersion of clonally related cells is a prominent feature of axis elongation in vertebrate embryos. Two major models have been proposed: (i) the intercalation of cells by convergent-extension and (ii) the sequential production of the forming axis by stem cells. The relative importance of both of these cell behaviors during the long period of elongation is poorly understood. Here, we use a combination of single cell lineage tracing in the mouse embryo, computer modeling and confocal video-microscopy of GFP labeled cells in the chick embryo to address the mechanisms involved in the antero-posterior dispersion of clones. In the mouse embryo, clones appear as clusters of labeled cells separated by intervals of non-labeled cells. The distribution of intervals between clonally related clusters correlates with a statistical model of a stem cell mode of growth only in the posterior spinal cord. A direct comparison with published data in zebrafish suggests that elongation of the anterior spinal cord involves similar intercalation processes in different vertebrate species. Time-lapse analyses of GFP labeled cells in cultured chick embryos suggest a decrease in the size of the neural progenitor pool and indicate that the dispersion of clones involves ordered changes of neighborhood relationships. We propose that a pre-existing stem zone of growth becomes predominant to form the posterior half of the axis. This temporal change in tissue-level motion is discussed in terms of the clonal and genetic continuities during axis elongation.

Impact of High-Frequency Stimulation Parameters on the Pattern of Discharge of Subthalamic Neurons

In clinical conditions, high-frequency stimulation (HFS) of subthalamic (STN) neurons in Parkinson's disease is empirically applied at ≥100 Hz (130–185 Hz), with pulses of short duration (60–100 μs) and 1- to 3-mA amplitude. Other parameter values produce no effect or aggravate the symptoms. To gain a better understanding of the mechanisms that underlie the therapeutic action of HFS, we have compared the effects of different combinations of parameter values delivered by clinical stimulators on the activity of STN neurons recorded in whole cell patch-clamp configuration in slices. We showed that none of tested combinations of parameters silenced the neurons. Non-therapeutic combinations i.e., low-frequency pulses (10–50 Hz), even at large amplitude or width, further excited the STN neurons with respect to their spontaneous activity. In contrast, combinations in the therapeutic range (80–185 Hz, 90–200 μs, 500–800 μA) replaced the preexisting activity by spikes, time-locked to the stimuli and thus presenting a striking regularity. When increasing pulse width or amplitude in this high-frequency range, the dual effect was still present but the activity generated became more irregular. We propose that during HFS at clinically relevant parameters, STN neurons behave as stable oscillators entirely driven by the stimulation, giving an average stable STN output that overrides spontaneous activity and introduces high-frequency regular spiking in the basal ganglia network.

The Mauthner cell half a century later: a neurobiological model for decision-making?

The Mauthner (M) cell is a critical element in a vital escape "reflex" triggered by abrupt or threatening events. Its properties at the molecular and synaptic levels, their various forms of plasticity, and the design of its networks, are all well adapted for this survival function. They guarantee that this behavior is appropriately unilateral, variable, and unpredictable. The M cell sets the behavioral threshold, and, acting in concert with other elements of the brainstem escape network, determines when, where, and how the escape is executed.

Dopamine modulation of spike dynamics in bursting neurons

The pyloric network of the lobster stomatogastric ganglion is a prime example of an oscillatory neural circuit. In our previous study on the firing patterns of pyloric neurons we observed characteristic temporal structures termed 'interspike interval (ISI) signatures' which were found to depend on the synaptic connectivity of the network. Dopamine, a well-known modulator of the pyloric network, is known to affect inhibitory synapses so it might also tune the fine temporal structure of intraburst spikes, a phenomenon not previously investigated. In the recent work we study the DA modulation of ISI patterns of two identified pyloric neurons in normal conditions and after blocking their glutamatergic synaptic connections. Dopamine (10-50 microM) strongly regularizes the firing of the lateral pyloric (LP) and pyloric dilator (PD) neurons by increasing the reliability of recurrent spike patterns. The most dramatic effect is observed in the LP, where precisely replicated spike multiplets appear in a normally 'noisy' neuron. The DA-induced regularization of intraburst spike patterns requires functional glutamatergic inputs to the LP neuron and this effect cannot be mimicked by simple intracellular depolarization. Inhibitory synaptic inputs arriving before the bursts are important factors in shaping the intraburst spike dynamics of both the PD and the LP neurons. Our data reveal a novel aspect of chemical neuromodulation in oscillatory neural networks. This effect sets in at concentrations lower than those affecting the overall burst pattern of the network. The sensitivity of intraburst spike dynamics to preceding synaptic inputs also suggests a novel method of temporal coding in neural bursters.

Is there chaos in the brain? II. Experimental evidence and related models

The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773-793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system. We first provide a short mathematical description of the models of excitable cells and of the different modes of firing of bursting neurons (Section 1). The deterministic behavior reported in giant axons (principally squid), in pacemaker cells, in isolated or in paired neurons of Invertebrates acting as coupled oscillators is then described (Section 2). We also consider chaotic processes exhibited by coupled Vertebrate neurons and of several components of Central Pattern Generators (Section 3). It is then shown that as indicated by studies of synaptic noise, deterministic patterns of firing in presynaptic interneurons are reliably transmitted, to their postsynaptic targets, via probabilistic synapses (Section 4). This raises the more general issue of chaos as a possible neuronal code and of the emerging concept of stochastic resonance Considerations on cortical dynamics and of EEGs are divided in two parts. The first concerns the early attempts by several pioneer authors to demonstrate chaos in experimental material such as the olfactory system or in human recordings during various forms of epilepsies, and the belief in 'dynamical diseases' (Section 5). The second part explores the more recent period during which surrogate-testing, definition of unstable periodic orbits and period-doubling bifurcations have been used to establish more firmly the nonlinear features of retinal and cortical activities and to define predictors of epileptic seizures (Section 6). Finally studies of multidimensional systems have founded radical hypothesis on the role of neuronal attractors in information processing, perception and memory and two elaborate models of the internal states of the brain (i.e. 'winnerless competition' and 'chaotic itinerancy'). Their modifications during cognitive functions are given special attention due to their functional and adaptive capabilities (Section 7) and despite the difficulties that still exist in the practical use of topological profiles in a state space to identify the physical underlying correlates. The reality of 'neurochaos' and its relations with information theory are discussed in the conclusion (Section 8) where are also emphasized the similarities between the theory of chaos and that of dynamical systems. Both theories strongly challenge computationalism and suggest that new models are needed to describe how the external world is represented in the brain.

Synaptic modulation of the interspike interval signatures of bursting pyloric neurons

The pyloric network of the lobster stomatogastric nervous system is one of the best described assemblies of oscillatory neurons producing bursts of action potentials. While the temporal patterns of bursts have been investigated in detail, those of spikes have received less attention. Here we analyze the intraburst firing patterns of pyloric neurons and the synaptic interactions shaping their dynamics in millisecond time scales not performed before. We find that different pyloric neurons express characteristic, cell-specific firing patterns in their bursts. Nonlinear analysis of the interspike intervals (ISIs) reveals distinctive temporal structures ('interspike interval signatures'), which are found to depend on the synaptic connectivity of the network. We compare ISI patterns of the pyloric dilator (PD), lateral pyloric (LP), and ventricular dilator (VD) neurons in 1) normal conditions, 2) after blocking glutamatergic synaptic connections, and 3) in various functional configurations of the three neurons. Manipulation of the synaptic connectivity results in characteristic changes in the ISI signatures of the postsynaptic neurons. The intraburst firing pattern of the PD neuron is regularized by the inhibitory synaptic connection from the LP neuron as revealed in current-clamp experiments and also as reconstructed with a dynamic clamp. On the other hand, mutual inhibition between the LP and VD neurons tend to produce more irregular bursts with increased spike jitter. The results show that synaptic interactions fine-tune the output of pyloric neurons. The present data also suggest a way of processing of synaptic information: bursting neurons are capable of encoding incoming signals by altering the fine structure of their intraburst spike patterns.

Time-dependent structure in the discharge rate of human motor units

OBJECTIVES

The aim of this study was to examine the influence of visual and motor processes on the deterministic and stochastic structure of force output and motor unit discharge variability.

METHODS

Young adult subjects produced continuous, isometric force at 3, 6, 12, and 24% of their maximal voluntary contraction at low and high visual gain levels through abduction of the index finger. Force and fine-wire intramuscular electromyography were recorded.

RESULTS

There was a linear increase in discharge irregularity with increases in the mean motor unit discharge rate (8-30 Hz). Recurrence analysis showed that the percentage of deterministic structure in discharge variability remained high, but decreased linearly with increased motor unit discharge rate. Surrogate analyses confirmed that the motor unit discharge variability was inconsistent with an uncorrelated and linearly correlated Gaussian noise process. Spectral analysis revealed that both the force output and the mean time-varying motor unit discharge time series had a dominant frequency of 0-2 Hz. Visual feedback gain did not affect the individual motor unit discharge patterns.

CONCLUSIONS

The motor unit discharge rate has deterministic time-dependent structure. The motor unit discharge rate is modulated at multiple time scales likely by pre- and post-synaptic induced fluctuations from spinal level pathways impinging on the motor neuron.

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.