Channel density regulation of firing patterns in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and downregulation or by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In this investigation we analyzed how the impulse patterns are regulated by the density of voltage-gated channels in a neuron model based on voltage-clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf-bifurcation threshold dynamics, respectively. Single, strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The relationship found here between channel densities and oscillatory behavior may partly explain the difference between the principal spiking patterns previously described for crab axons (class 1 and 2) and cortical neurons (regular firing and fast spiking).     

Role of neurotrophin signalling in the differentiation of neurons from dorsal root ganglia and sympathetic ganglia

Manipulation of neurotrophin (NT) signalling by administration or depletion of NTs, by transgenic overexpression or by deletion of genes coding for NTs and their receptors has demonstrated the importance of NT signalling for the survival and differentiation of neurons in sympathetic and dorsal root ganglia (DRG). Combination with mutation of the proapoptotic Bax gene allows the separation of survival and differentiation effects. These studies together with cell culture analysis suggest that NT signalling directly regulates the differentiation of neuron subpopulations and their integration into neural networks. The high-affinity NT receptors trkA, trkB and trkC are restricted to subpopulations of mature neurons, whereas their expression at early developmental stages largely overlaps. trkC is expressed throughout sympathetic ganglia and DRG early after ganglion formation but becomes restricted to small neuron subpopulations during embryogenesis when trkA is turned on. The temporal relationship between trkA and trkC expression is conserved between sympathetic ganglia and DRG. In DRG, NGF signalling is required not only for survival, but also for the differentiation of nociceptors. Expression of neuropeptides calcitonin gene-related peptide and substance P, which specify peptidergic nociceptors, depends on nerve growth factor (NGF) signalling. ret expression indicative of non-peptidergic nociceptors is also promoted by the NGF-signalling pathway. Regulation of TRP channels by NGF signalling might specify the temperature sensitivity of afferent neurons embryonically. The manipulation of NGF levels “tunes” heat sensitivity in nociceptors at postnatal and adult stages. Brain-derived neurotrophic factor signalling is required for subpopulations of DRG neurons that are not fully characterized; it affects mechanical sensitivity in slowly adapting, low-threshold mechanoreceptors and might involve the regulation of DEG/ENaC ion channels. NT3 signalling is required for the generation and survival of various DRG neuron classes, in particular proprioceptors. Its importance for peripheral projections and central connectivity of proprioceptors demonstrates the significance of NT signalling for integrating responsive neurons in neural networks. The molecular targets of NT3 signalling in proprioceptor differentiation remain to be characterized. In sympathetic ganglia, NGF signalling regulates dendritic development and axonal projections. Its role in the specification of other neuronal properties is less well analysed. In vitro analysis suggests the involvement of NT signalling in the choice between the noradrenergic and cholinergic transmitter phenotype, in the expression of various classes of ion channels and for target connectivity. In vivo analysis is required to show the degree to which NT signalling regulates these sympathetic neuron properties in developing embryos and postnatally. U.E. is supported by the DFG (Er145-4) and the Gemeinnützige Hertie-Stiftung.     

Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and down-regulation, by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In the present investigation, we analyze how the impulse patterns are regulated by the density of voltage-gated channels in a model neuron, based on voltage clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf bifurcation threshold dynamics, respectively. Single strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The presently found relationship between channel densities and oscillatory behavior may be relevance for understanding principal spiking patterns of cortical neurons (regular firing and fast spiking). It may also be of relevance for understanding the action of pharmacological compounds on brain oscillatory activity.     

Neuronal Mechanisms Encoding Global-to-Fine Information in Inferior-Temporal Cortex

Sugase et al. found that global information is represented at the initial transient firing of a single face-responsive neuron in inferior-temporal (IT) cortex, and that finer information is represented at the subsequent sustained firing. A feed-forward model and an attractor network are conceivable models to reproduce this dynamics. The attractor network, specifically an associative memory model, is employed to elucidate the neuronal mechanisms producing the dynamics. The results obtained by computer simulations show that a state of neuronal population initially approaches to a mean state of similar memory patterns, and that it finally converges to a memory pattern. This dynamics qualitatively coincides with that of face-responsive neurons. The dynamics of a single neuron in the model also coincides with that of a single face-responsive neuron. Furthermore, we propose two physiological experiments and predict the results from our model. Both predicted results are not explainable by the feed-forward model. Therefore, if the results obtained by actual physiological experiments coincide with our predicted results, the attractor network might be the neuronal mechanisms producing the dynamics of face-responsive neurons.     

On the role of anatomy in learning by the cerebellar cortex

The properties due to the location of neurons, synapses, and possibly even synaptic channels, in neuron networks are still unknown. Our preliminary results suggest that not only the interconnections but also the relative positions of the different elements in the network are of importance in the learning process in the cerebellar cortex. We have used neural field equations to investigate the mechanisms of learning in the hierarchical neural network. The numerical resolution of these equations reveals two important properties: (i) The hierarchical structure of this network has the expected effect on learning because the flow of information at the neuronal level is controlled by the heterosynaptic effect through the synaptic density-connectivity function, i.e. the action potential field variable is controlled by the synaptic efficacy field variable at different points of the neuron. (ii) The geometry of the system involves different velocities of propagation along different fibers, i.e. different delays between cells, and thus has a stabilizing effect on the dynamics, allowing the Purkinje output to reach a given value. The field model proposed should be useful in the study of the spatial properties of hierarchical biological systems.     

A Change in the Ion Selectivity of Ligand-Gated Ion Channels Provides a Mechanism to Switch Behavior

Behavioral output of neural networks depends on a delicate balance between excitatory and inhibitory synaptic connections. However, it is not known whether network formation and stability is constrained by the sign of synaptic connections between neurons within the network. Here we show that switching the sign of a synapse within a neural circuit can reverse the behavioral output. The inhibitory tyramine-gated chloride channel, LGC-55, induces head relaxation and inhibits forward locomotion during the Caenorhabditis elegans escape response. We switched the ion selectivity of an inhibitory LGC-55 anion channel to an excitatory LGC-55 cation channel. The engineered cation channel is properly trafficked in the native neural circuit and results in behavioral responses that are opposite to those produced by activation of the LGC-55 anion channel. Our findings indicate that switches in ion selectivity of ligand-gated ion channels (LGICs) do not affect network connectivity or stability and may provide an evolutionary and a synthetic mechanism to change behavior.     

Intrinsic Functional Hypoconnectivity in Core Neurocognitive Networks Suggests Central Nervous System Pathology in Patients with Myalgic Encephalomyelitis: A Pilot Study

Exact low resolution electromagnetic tomography (eLORETA) was recorded from nineteen EEG channels in nine patients with myalgic encephalomyelitis (ME) and 9 healthy controls to assess current source density and functional connectivity, a physiological measure of similarity between pairs of distributed regions of interest, between groups. Current source density and functional connectivity were measured using eLORETA software. We found significantly decreased eLORETA source analysis oscillations in the occipital, parietal, posterior cingulate, and posterior temporal lobes in Alpha and Alpha-2. For connectivity analysis, we assessed functional connectivity within Menon triple network model of neuropathology. We found support for all three networks of the triple network model, namely the central executive network (CEN), salience network (SN), and the default mode network (DMN) indicating hypo-connectivity in the Delta, Alpha, and Alpha-2 frequency bands in patients with ME compared to controls. In addition to the current source density resting state dysfunction in the occipital, parietal, posterior temporal and posterior cingulate, the disrupted connectivity of the CEN, SN, and DMN appears to be involved in cognitive impairment for patients with ME. This research suggests that disruptions in these regions and networks could be a neurobiological feature of the disorder, representing underlying neural dysfunction.     

Mechanisms of Gain Control by Voltage-Gated Channels in Intrinsically-Firing Neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.     

Activity dependent degeneration explains hub vulnerability in Alzheimer's disease

Brain connectivity studies have revealed that highly connected 'hub' regions are particularly vulnerable to Alzheimer pathology: they show marked amyloid-β deposition at an early stage. Recently, excessive local neuronal activity has been shown to increase amyloid deposition. In this study we use a computational model to test the hypothesis that hub regions possess the highest level of activity and that hub vulnerability in Alzheimer's disease is due to this feature. Cortical brain regions were modeled as neural masses, each describing the average activity (spike density and spectral power) of a large number of interconnected excitatory and inhibitory neurons. The large-scale network consisted of 78 neural masses, connected according to a human DTI-based cortical topology. Spike density and spectral power were positively correlated with structural and functional node degrees, confirming the high activity of hub regions, also offering a possible explanation for high resting state Default Mode Network activity. 'Activity dependent degeneration' (ADD) was simulated by lowering synaptic strength as a function of the spike density of the main excitatory neurons, and compared to random degeneration. Resulting structural and functional network changes were assessed with graph theoretical analysis. Effects of ADD included oscillatory slowing, loss of spectral power and long-range synchronization, hub vulnerability, and disrupted functional network topology. Observed transient increases in spike density and functional connectivity match reports in Mild Cognitive Impairment (MCI) patients, and may not be compensatory but pathological. In conclusion, the assumption of excessive neuronal activity leading to degeneration provides a possible explanation for hub vulnerability in Alzheimer's disease, supported by the observed relation between connectivity and activity and the reproduction of several neurophysiologic hallmarks. The insight that neuronal activity might play a causal role in Alzheimer's disease can have implications for early detection and interventional strategies.     

Recurrent fractal neural networks: a strategy for the exchange of local and global information processing in the brain

The regulation of biological networks relies significantly on convergent feedback signaling loops that render a global output locally accessible. Ideally, the recurrent connectivity within these systems is self-organized by a time-dependent phase-locking mechanism. This study analyzes recurrent fractal neural networks (RFNNs), which utilize a self-similar or fractal branching structure of dendrites and downstream networks for phase-locking of reciprocal feedback loops: output from outer branch nodes of the network tree enters inner branch nodes of the dendritic tree in single neurons. This structural organization enables RFNNs to amplify re-entrant input by over-the-threshold signal summation from feedback loops with equivalent signal traveling times. The columnar organization of pyramidal neurons in the neocortical layers V and III is discussed as the structural substrate for this network architecture. RFNNs self-organize spike trains and render the entire neural network output accessible to the dendritic tree of each neuron within this network. As the result of a contraction mapping operation, the local dendritic input pattern contains a downscaled version of the network output coding structure. RFNNs perform robust, fractal data compression, thus coping with a limited number of feedback loops for signal transport in convergent neural networks. This property is discussed as a significant step toward the solution of a fundamental problem in neuroscience: how is neuronal computation in separate neurons and remote brain areas unified as an instance of experience in consciousness? RFNNs are promising candidates for engaging neural networks into a coherent activity and provide a strategy for the exchange of global and local information processing in the human brain, thereby ensuring the completeness of a transformation from neuronal computation into conscious experience.     

Numerical exploration of the influence of neural noise on the psychometric function at low stimulation intensity levels

The relationship between stimulus intensity and the probability of detecting the presence of the stimulus is described by the psychometrical function. The probabilistic nature of this relationship is based on the stochastic behaviour of sensory neural channels and sensory networks involved in perceptual processing (Kiang 1968). This study tries to establish a continuum of variability across different levels of integration in the central nervous system. Once the opening and closing times of ionic channels was simulated, a threshold to the collective behaviour of voltage-gated ionic channels was imposed in order to generate the spike train of a single neuron. Afterwards, the trains of spikes of different neurons were added up, simulating the activity of a sensory nerve. By adding the activity due to the stimulus to the spontaneous neural behaviour, the psychometric function was simulated using a thresholding approach. The results can replicate the stochastic resonance phenomenon, but also open up the possibility that attentional phenomena can be mediated not only by increasing neural activity (bursting or oscillatory), but also by increasing noise at the neural level.     

3D multicolor super-resolution imaging offers improved accuracy in neuron tracing

The connectivity among neurons holds the key to understanding brain function. Mapping neural connectivity in brain circuits requires imaging techniques with high spatial resolution to facilitate neuron tracing and high molecular specificity to mark different cellular and molecular populations. Here, we tested a three-dimensional (3D), multicolor super-resolution imaging method, stochastic optical reconstruction microscopy (STORM), for tracing neural connectivity using cultured hippocampal neurons obtained from wild-type neonatal rat embryos as a model system. Using a membrane specific labeling approach that improves labeling density compared to cytoplasmic labeling, we imaged neural processes at 44 nm 2D and 116 nm 3D resolution as determined by considering both the localization precision of the fluorescent probes and the Nyquist criterion based on label density. Comparison with confocal images showed that, with the currently achieved resolution, we could distinguish and trace substantially more neuronal processes in the super-resolution images. The accuracy of tracing was further improved by using multicolor super-resolution imaging. The resolution obtained here was largely limited by the label density and not by the localization precision of the fluorescent probes. Therefore, higher image resolution, and thus higher tracing accuracy, can in principle be achieved by further improving the label density.     

Stochastic resonance of localized activity driven by common noise

We study the influence of spatially correlated noise on the transient dynamics of a recurrent network with Mexican-Hat-type connectivity. We derive the closed form of the order parameter functional in the thermodynamical limit of neuron number N. Our analysis shows that network dynamics is qualitatively changed by the presence of common noise. Network dynamics driven by common noise obtains the global level of fluctuation, which is not observed in a network driven by independent noise only. We show that the optimal level of global fluctuation enhances the transition from non-localized firing states to spatially localized firing states, and also enhances the rotation speed of localized activity.     

Differential subcellular distribution of ion channels and the diversity of neuronal function

Following the astonishing molecular diversity of voltage-gated ion channels that was revealed in the past few decades, the ion channel repertoire expressed by neurons has been implicated as the major factor governing their functional heterogeneity. Although the molecular structure of ion channels is a key determinant of their biophysical properties, their subcellular distribution and densities on the surface of nerve cells are just as important for fulfilling functional requirements. Recent results obtained with high resolution quantitative localization techniques revealed complex, subcellular compartment-specific distribution patterns of distinct ion channels. Here I suggest that within a given neuron type every ion channel has a unique cell surface distribution pattern, with the functional consequence that this dramatically increases the computational power of nerve cells.     

The Xenopus retinal ganglion cell as a model neuron to study the establishment of neuronal connectivity

Neurons receive inputs through their multiple branched dendrites and pass this information on to the next neuron via long axons, which branch within the target. The shape the neuron acquires is thus the key to its proper functioning in the neural circuit in which it participates. Both axons and dendrites grow in a directed fashion to their target partner neurons by responding to a large number of molecular cues in the milieu through which they extend. They then go through the process of synaptogenesis, first choosing a neuron on which to synapse, and then the appropriate subcellular location. How a neuron acquires its unique shape, establishes and modifies appropriate synaptic connectivity, and the molecular signals involved, are key questions in developmental neurobiology. Such questions of nervous system wiring are being pursued actively with a variety of different animal models and neuron types, each with its own unique advantages. Among these, the developing retinal ganglion cell (RGC) of the South African clawed frog, Xenopus laevis, has proven particularly fruitful for revealing the secrets of how axons and dendrites acquire their final morphology and connectivity. In this review, we describe how this system can be used to understand the multiple molecular events that instruct the incorporation of RGCs into the neural circuit that controls vision.     

Role of type-specific neuron properties in a spinal cord motor network

Recent recordings from spinal neurons in hatchling frog tadpoles allow their type-specific properties to be defined. Seven main types of neuron involved in the control of swimming have been characterized. To investigate the significance of type-specific properties, we build models of each neuron type and assemble them into a network using known connectivity between: sensory neurons, sensory pathway interneurons, central pattern generator (CPG) interneurons and motoneurons. A single stimulus to a sensory neuron initiates swimming where modelled neuronal and network activity parallels physiological activity. Substitution of firing properties between neuron types shows that those of excitatory CPG interneurons are critical for stable swimming. We suggest that type-specific neuronal properties can reflect the requirements for involvement in one particular network response (like swimming), but may also reflect the need to participate in more than one response (like swimming and slower struggling). Action Editor: Eberhard E. Fetz     

Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.     

New optical tools for controlling neuronal activity

A major challenge in understanding the relationship between neural activity and development, and ultimately behavior, is to control simultaneously the activity of either many neurons belonging to specific subsets or specific regions within individual neurons. Optimally, such a technique should be capable of both switching nerve cells on and off within milliseconds in a non-invasive manner, and inducing depolarizations or hyperpolarizations for periods lasting from milliseconds to many seconds. Specific ion conductances in subcellular compartments must also be controlled to bypass signaling cascades in order to regulate precisely cellular events such as synaptic transmission. Light-activated G-protein-coupled receptors and ion channels, which can be genetically manipulated and targeted to neuronal circuits, have the greatest potential to fulfill these requirements.