Communication in neuronal networks

Axon Initial Segment Kv1 Channels Control Axonal Action Potential Waveform and Synaptic Efficacy

Action potentials are binary signals that transmit information via their rate and temporal pattern. In this context, the axon is thought of as a transmission line, devoid of a role in neuronal computation. Here, we show a highly localized role of axonal Kv1 potassium channels in shaping the action potential waveform in the axon initial segment (AIS) of layer 5 pyramidal neurons independent of the soma. Cell-attached recordings revealed a 10-fold increase in Kv1 channel density over the first 50 microm of the AIS. Inactivation of AIS and proximal axonal Kv1 channels, as occurs during slow subthreshold somatodendritic depolarizations, led to a distance-dependent broadening of axonal action potentials, as well as an increase in synaptic strength at proximal axonal terminals. Thus, Kv1 channels are strategically positioned to integrate slow subthreshold signals, providing control of the presynaptic action potential waveform and synaptic coupling in local cortical circuits.

Social network theory in the behavioural sciences: potential applications

Social network theory has made major contributions to our understanding of human social organisation but has found relatively little application in the field of animal behaviour. In this review, we identify several broad research areas where the networks approach could greatly enhance our understanding of social patterns and processes in animals. The network theory provides a quantitative framework that can be used to characterise social structure both at the level of the individual and the population. These novel quantitative variables may provide a new tool in addressing key questions in behavioural ecology particularly in relation to the evolution of social organisation and the impact of social structure on evolutionary processes. For example, network measures could be used to compare social networks of different species or populations making full use of the comparative approach. However, the networks approach can in principle go beyond identifying structural patterns and also can help with the understanding of processes within animal populations such as disease transmission and information transfer. Finally, understanding the pattern of interactions in the network (i.e. who is connected to whom) can also shed some light on the evolution of behavioural strategies.

Mapping human whole-brain structural networks with diffusion MRI

Understanding the large-scale structural network formed by neurons is a major challenge in system neuroscience. A detailed connectivity map covering the entire brain would therefore be of great value. Based on diffusion MRI, we propose an efficient methodology to generate large, comprehensive and individual white matter connectional datasets of the living or dead, human or animal brain. This non-invasive tool enables us to study the basic and potentially complex network properties of the entire brain. For two human subjects we find that their individual brain networks have an exponential node degree distribution and that their global organization is in the form of a small world.

Stochastic simulations on the reliability of action potential propagation in thin axons

It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 microm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 microm diameter are reliable.

The function of intersegmental connections in determining temporal characteristics of the spinal cord rhythmic output

Recent renewed interest in the study of rhythmic behaviors and pattern-generating circuits has been inspired by the currently well-established role of oscillating neuronal networks in all aspects of the function of our nervous system: from sensory integration to central processing, and of course motor control. An integrative rather than reductionist approach in the study of pattern-generating circuits is in accordance with current developments. The lamprey spinal cord, a relatively simple and much-studied preparation, is a useful model for such a study. It is an example of a chain of coupled oscillatory units that is characterized by its ability to demonstrate robust coordinated rhythmic output when isolated in vitro. The preparation allows maximum control over the chemical (neuromodulators and hormones) as well as neuronal environment (sensory and descending inputs) of the single oscillatory unit: the pattern-generating circuit. The current study made use of recently developed tools for nonlinear analysis of time-series, specifically neurophysiological signals. These tools allow us to reveal and characterize biological-functional complexity and information capacity of the neuronal output recorded from the lamprey model network. We focused on the importance of different types of inputs to an oscillatory network and their effect on the network's functional output. We show that the basic circuit, when isolated from short- and long-range neuronal inputs, demonstrates its full potential of information capacity: maximal variation quantities and elevated functional complexity. Morphological and functional constraints result in the network exhibiting only a limited range of the above. This constitutes an important substrate for plasticity in neuronal network function.

Small-world network topology of hippocampal neuronal network is lost, in an in vitro glutamate injury model of epilepsy

Neuronal network topologies and connectivity patterns were explored in control and glutamate-injured hippocampal neuronal networks, cultured on planar multielectrode arrays. Spontaneous activity was characterized by brief episodes of synchronous firing at many sites in the array (network bursts). During such assembly activity, maximum numbers of neurons are known to interact in the network. After brief glutamate exposure followed by recovery, neuronal networks became hypersynchronous and fired network bursts at higher frequency. Connectivity maps were constructed to understand how neurons communicate during a network burst. These maps were obtained by analysing the spike trains using cross-covariance analysis and graph theory methods. Analysis of degree distribution, which is a measure of direct connections between electrodes in a neuronal network, showed exponential and Gaussian distributions in control and glutamate-injured networks, respectively. Although both the networks showed random features, small-world properties in these networks were different. These results suggest that functional two-dimensional neuronal networks in vitro are not scale-free. After brief exposure to glutamate, normal hippocampal neuronal networks became hyperexcitable and fired a larger number of network bursts with altered network topology. The small-world network property was lost and this was accompanied by a change from an exponential to a Gaussian network.

Beta- and gamma-frequency coupling between olfactory and motor brain regions prior to skilled, olfactory-driven reaching

A major question in neuroscience concerns how widely separated brain regions coordinate their activity to produce unitary cognitive states or motor actions. To investigate this question, we employed multisite, multielectrode recording in rats to study how olfactory and motor circuits are coupled prior to the execution of an olfactory-driven, GO/NO-GO variant of a skilled, rapidly executed (approximately 350-600 ms) reaching task. During task performance, we recorded multi-single units and local field potentials (LFPs) simultaneously from the rats' olfactory cortex (specifically, the posterior piriform cortex) and from cortical and subcortical motor sites (the caudal forepaw M1, and the magnocellular red nucleus, respectively). Analyses on multi-single units across areas revealed an increase in beta-frequency spiking (12-30 Hz) during a approximately 100 ms window surrounding the Final Sniff of the GO cue before lifting the arm (the "Sniff-GO window") that was seldom seen when animals sniffed the NO-GO cue. Also during the Sniff-GO window, LFPs displayed a striking increase in beta, low-gamma, and high-gamma energy (12-30, 30-50, and 50-100 Hz, respectively), and oscillations in the high gamma band appeared to be coherent across the recorded sites. These results indicate that transient, multispectral coherence across cortical and subcortical brain sites is part of the coordination process prior to sensory-guided movement initiation.

A scale-free systems theory of motivation and addiction

Scale-free organizations, characterized by uneven distributions of linkages between nodal elements, describe the structure and function of many life-based complex systems developing under evolutionary pressures. We explore motivated behavior as a scale-free map toward a comprehensive translational theory of addiction. Motivational and behavioral repertoires are reframed as link and nodal element sets, respectively, comprising a scale-free structure. These sets are generated by semi-independent information-processing streams within cortical-striatal circuits that cooperatively provide decision-making and sequential processing functions necessary for traversing maps of motivational links connecting behavioral nodes. Dopamine modulation of cortical-striatal plasticity serves a central-hierarchical mechanism for survival-adaptive sculpting and development of motivational-behavioral repertoires by guiding a scale-free design. Drug-induced dopamine activity promotes drug taking as a highly connected behavioral hub at the expense of natural-adaptive motivational links and behavioral nodes. Conceptualizing addiction as pathological alteration of scale-free motivational-behavioral repertoires unifies neurobiological, neurocomputational and behavioral research while addressing addiction vulnerability in adolescence and psychiatric illness. This model may inform integrative research in defining more effective prevention and treatment strategies for addiction.

Pain Enhances Functional Connectivity of a Brain Network Evoked by Performance of a Cognitive Task

Experimental and clinical evidence indicates that pain can affect cognitive processes, but the cortical networks involved in pain-cognition interactions are unclear. In this study, we determined the effect of pain on the activity of cortical areas involved in cognition acting as a whole (i.e., a network). Subjects underwent functional magnetic resonance imaging (fMRI) while engaged in an attention-demanding cognitive task (multisource interference task) of varying difficulty and simultaneously receiving painful stimuli at varying intensities. The control (baseline) condition was simple finger tapping that had minimal cognitive demands and without pain. Functional connectivity analysis revealed a cortical network consisting of two anti-correlated parts: a task-negative part (precuneus/posterior cingulate cortex, medial frontal and inferior parietal/temporal) the activity of which correlated negatively with the cognitive task and positively with the control baseline, and a task-positive part (inferior frontal, superior parietal, premotor, and anterior insula cortices) the activity of which correlated positively with the cognitive task and negatively with the baseline. Independent components analysis revealed these opposing networks were operating at a low frequency (0.03–0.08 Hz). The functional connectivity of the task-positive network was increased by cognitive demand and by pain. We suggest this attention-specific network balances the needs of general self-referential and environmental awareness versus focused attention to salient information. We postulate that pain affects cognitive ability by its reliance on this common attention-specific network. These data provide evidence that pain can modulate a network presumed to be involved in focused attention, suggesting a mechanism for the interference of pain on cognitive ability by the consumption of attentional resources.

Statistical geometric affinity in human brain electric activity

The representation of the human electroencephalogram (EEG) records by neurophysiologists demands standardized time-amplitude scales for their correct conventional interpretation. In a suite of graphical experiments involving scaling affine transformations we have been able to convert electroencephalogram samples corresponding to any particular sleep phase and relaxed wakefulness into each other. We propound a statistical explanation for that finding in terms of data collapse. As a sequel, we determine characteristic time and amplitude scales and outline a possible physical interpretation. An analysis for characteristic times based on lacunarity is also carried out as well as a study of the synchrony between left and right EEG channels.

Energy coding in biological neural networks

According to the experimental result of signal transmission and neuronal energetic demands being tightly coupled to information coding in the cerebral cortex, we present a brand new scientific theory that offers an unique mechanism for brain information processing. We demonstrate that the neural coding produced by the activity of the brain is well described by our theory of energy coding. Due to the energy coding model's ability to reveal mechanisms of brain information processing based upon known biophysical properties, we can not only reproduce various experimental results of neuro-electrophysiology, but also quantitatively explain the recent experimental results from neuroscientists at Yale University by means of the principle of energy coding. Due to the theory of energy coding to bridge the gap between functional connections within a biological neural network and energetic consumption, we estimate that the theory has very important consequences for quantitative research of cognitive function.

Efficiency and cost of economical brain functional networks

Brain anatomical networks are sparse, complex, and have economical small-world properties. We investigated the efficiency and cost of human brain functional networks measured using functional magnetic resonance imaging (fMRI) in a factorial design: two groups of healthy old (N = 11; mean age = 66.5 years) and healthy young (N = 15; mean age = 24.7 years) volunteers were each scanned twice in a no-task or "resting" state following placebo or a single dose of a dopamine receptor antagonist (sulpiride 400 mg). Functional connectivity between 90 cortical and subcortical regions was estimated by wavelet correlation analysis, in the frequency interval 0.06-0.11 Hz, and thresholded to construct undirected graphs. These brain functional networks were small-world and economical in the sense of providing high global and local efficiency of parallel information processing for low connection cost. Efficiency was reduced disproportionately to cost in older people, and the detrimental effects of age on efficiency were localised to frontal and temporal cortical and subcortical regions. Dopamine antagonism also impaired global and local efficiency of the network, but this effect was differentially localised and did not interact with the effect of age. Brain functional networks have economical small-world properties-supporting efficient parallel information transfer at relatively low cost-which are differently impaired by normal aging and pharmacological blockade of dopamine transmission.

Neuronal coherence during selective attentional processing and sensory-motor integration

Groups of neurons synchronize their activities during a variety of conditions, but whether this synchronization is functionally relevant has remained a matter of debate. Here, we survey recent findings showing that synchronization is dynamically modulated during cognitive processes. Based on this evidence, synchronization appears to reflect a general mechanism that renders interactions among selective subsets of neurons effective. We show that neuronal synchronization predicts which sensory input is processed and how efficient it is transmitted to postsynaptic target neurons during sensory-motor integration. Four lines of evidence are presented supporting the hypothesis that rhythmic neuronal synchronization, also called neuronal coherence, underlies effective and selective neuronal communication. (1) Findings from intracellular recordings strongly suggest that postsynaptic neurons are particularly sensitive to synaptic input that is synchronized in the gamma-frequency (30-90 Hz) range. (2) Neurophysiological studies in awake animals revealed enhanced rhythmic synchronization among neurons encoding task-relevant information. (3) The trial-by-trial variation in the precision of neuronal synchronization predicts part of the trial-by-trial variation in the speed of visuo-motor integration. (4) The planning and selection of specific movements can be predicted by the strength of coherent oscillations among local neuronal groups in frontal and parietal cortex. Thus, neuronal coherence appears as a neuronal substrate of an effective neuronal communication structure that dynamically links neurons into functional groups processing task-relevant information and selecting appropriate actions during attention and effective sensory-motor integration.

Sensory-evoked intrinsic optical signals in the olfactory bulb are coupled to glutamate release and uptake

Functional imaging signals arise from metabolic and hemodynamic activity, but how these processes are related to the synaptic and electrical activity of neurons is not well understood. To provide insight into this issue, we used in vivo imaging and simultaneous local pharmacology to study how sensory-evoked neural activity leads to intrinsic optical signals (IOS) in the well-defined circuitry of the olfactory glomerulus. Odor-evoked IOS were tightly coupled to release of glutamate and were strongly modulated by activation of presynaptic dopamine and GABA-B receptors. Surprisingly, IOS were independent of postsynaptic transmission through ionotropic or metabotropic glutamate receptors, but instead were inhibited when uptake by astrocytic glutamate transporters was blocked. These data suggest that presynaptic glutamate release and uptake by astrocytes form a critical pathway through which neural activity is linked to metabolic processing and hence to functional imaging signals.

Role of transport performance for neuron cell morphology

The compartmental model is a basic tool for studying signal propagation in neurons; if the model parameters are adequately redefined, it can also be helpful in the study of electrical or fluid transport in other biological systems. Here we show that the input resistance in different networks that simulate the morphology of neurons is the result of the interplay between the relevant conductances, neuron morphology, and neuron size. The results suggest that neurons may grow in such a way that facilitates the current flow to the synapses, concurrently minimizing power consumption.

A Comparison Study of the Vertical Bias of Pyramidal Cells in the Hippocampus and Neocortex

In this study, we employed morphometric image analysis of the hippocampus proper and temporal lobe neocortex in postmortem tissue to determine vertical bias quantified as Deltatheta, angular dispersion, as well asan index of alignment of cellular elements relative to the radial plane. The radial alignment of cellular elements was consistent with a minicolumnar organization of the cortex. Photomicrographs were taken of the left-hemisphere hippocampal CA3/1 subfields of 13 fetal subjects ranging in gestational age from 19 weeks to 36 weeks and 19 normal individuals aged 4 months to 98 years. For comparison, micrographs from the temporal lobe (Brodmann areas 21 and 22) were similarly processed for layers III and V, where the x-axes of the transformed coordinate system were taken to be the layer III/IV and IV/V borders, respectively. Computerized image analysis measurements of the angular dispersion for the temporal lobe region and hippocampus proper differed significantly within the same brains (p < 0.001). The neocortical layer III exhibited the highest values for Deltatheta, indicating a high degree of columnar organization. Values for Deltatheta in the hippocampal CA subfields were lower but demonstrated significance for the radial alignment of neurons in this area. Values for Deltathetain layer V were intermediate between those of layer III and the hippocampus, consistent with increasing degrees of radial columnar organization of infragranular layers of the neocortex in comparison with the hippocampus and of supragranular in comparison with infragranular neocortical layers. Pyramidal cell arrays within allocortical areas and the neocortex constitute different modular arrangements. This morphological variability may be the expression of evolutionary differences in cortical development.

Gamma band oscillations reveal neural network cortical coherence dysfunction in schizophrenia patients

BACKGROUND

Gamma band activity has been associated with many sensory and cognitive functions, and is important for cortico-cortical transmission and the integration of information across neural networks. The aims of the present study were to determine if schizophrenia patients have deficits in the generation and maintenance of coherent, synchronized oscillations in response to steady-state stimulation, and to examine the clinical and cognitive correlates of the electroencephalography (EEG) oscillatory dynamics.

METHODS

Schizophrenia patients (n = 100) and nonpsychiatric subjects (n = 80) underwent auditory steady-state event-related potential testing. Click trains varying in rate of stimulation (20, 30, and 40 Hz) were presented; EEG-evoked power and intertrial phase synchronization were obtained in response to each stimulation frequency. Subjects also underwent clinical and neurocognitive assessments.

RESULTS

Patients had reductions in both evoked power and phase synchronization in response to 30- and 40-Hz stimulation but normal responsivity to 20-Hz stimulation. Maximal deficits were detected in response to 40-Hz stimulation. A modest association of reduced working memory performance and 40-Hz intertrial phase synchronization was present in schizophrenia patients (r = .32, p <.01).

CONCLUSIONS

Schizophrenia patients have frequency-specific deficits in the generation and maintenance of coherent gamma-range oscillations, reflecting a fundamental degradation of basic integrated neural network activity.

Neuropathological and genetic findings in autism: the significance of a putative minicolumnopathy

Autism is a condition manifested as abnormalities of relatedness, communication, range of interests, and repetitive behaviors. Despite alarming prevalence estimates and exhortations to research, little is known regarding its pathophysiology. Recent reports of a putative minicolumnopathy explain changes in brain size, gray/white matter ratios, and interareal connectivity. This article summarizes possible links between minicolumns and other topics-cortical modularity, age of onset, gliosis, and genetics-relevant to the pathophysiology of autism.

A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields

Computational models of primary visual cortex have demonstrated that principles of efficient coding and neuronal sparseness can explain the emergence of neurones with localised oriented receptive fields. Yet, existing models have failed to predict the diverse shapes of receptive fields that occur in nature. The existing models used a particular "soft" form of sparseness that limits average neuronal activity. Here we study models of efficient coding in a broader context by comparing soft and "bard" forms of neuronal sparseness. As a result of our analyses, we propose a novel network model for visual cortex. The model forms efficient visual representations in which the number of active neurones, rather than mean neuronal activity, is limited. This form of hard sparseness also economises cortical resources like synaptic memory and metabolic energy. Furthermore, our model accurately predicts the distribution of receptive field shapes found in the primary visual cortex of cat and monkey.

Minicolumnar abnormalities in autism

Autism is characterized by qualitative abnormalities in behavior and higher order cognitive functions. Minicolumnar irregularities observed in autism provide a neurologically sound localization to observed clinical and anatomical abnormalities. This study corroborates the initial reports of a minicolumnopathy in autism within an independent sample. The patient population consisted of six age-matched pairs of patients (DSM-IV-TR and ADI-R diagnosed) and controls. Digital micrographs were taken from cortical areas S1, 4, 9, and 17. The image analysis produced estimates of minicolumnar width (CW), mean interneuronal distance, variability in CW (V (CW)), cross section of Nissl-stained somata, boundary length of stained somata per unit area, and the planar convexity. On average CW was 27.2 microm in controls and 25.7 microm in autistic patients (P = 0.0234). Mean neuron and nucleolar cross sections were found to be smaller in autistic cases compared to controls, while neuron density in autism exceeded the comparison group by 23%. Analysis of inter- and intracluster distances of a Delaunay triangulation suggests that the increased cell density is the result of a greater number of minicolumns, otherwise the number of cells per minicolumns appears normal. A reduction in both somatic and nucleolar cross sections could reflect a bias towards shorter connecting fibers, which favors local computation at the expense of inter-areal and callosal connectivity.

Sparse representations for the cocktail party problem

A striking feature of many sensory processing problems is that there appear to be many more neurons engaged in the internal representations of the signal than in its transduction. For example, humans have approximately 30,000 cochlear neurons, but at least 1000 times as many neurons in the auditory cortex. Such apparently redundant internal representations have sometimes been proposed as necessary to overcome neuronal noise. We instead posit that they directly subserve computations of interest. Here we provide an example of how sparse overcomplete linear representations can directly solve difficult acoustic signal processing problems, using as an example monaural source separation using solely the cues provided by the differential filtering imposed on a source by its path from its origin to the cochlea [the head-related transfer function (HRTF)]. In contrast to much previous work, the HRTF is used here to separate auditory streams rather than to localize them in space. The experimentally testable predictions that arise from this model, including a novel method for estimating the optimal stimulus of a neuron using data from a multineuron recording experiment, are generic and apply to a wide range of sensory computations.

Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems

It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths, rather than wiring length. These findings suggest that neural systems are not exclusively optimized for minimal global wiring, but for a variety of factors including the minimization of processing steps.

Comparative gene expression analysis reveals a characteristic molecular profile of the superior olivary complex

The superior olivary complex (SOC) is a very conspicuous structure in the mammalian auditory brainstem. It represents the first binaural processing center and is important for sound localization in the azimuth and in feedback regulation of cochlear function. In order to define molecular determinants of the SOC, which are of potential functional relevance, we have performed a comprehensive analysis of its transcriptome by serial analysis of gene expression in adult rats. Here, we performed a detailed analysis of the SOC's gene expression profile compared to that of two other neural tissues, the striatum and the hippocampus, and with extraocular muscle tissue. This tested the hypothesis that SOC-specific or significantly upregulated transcripts provide candidates for the specific function of auditory neurons. Thirty-three genes were significantly upregulated in the SOC when compared to the two other neural tissues. Thirteen encoded proteins involved in neurotransmission, including action potential propagation, exocytosis, and myelination; five genes are important for the energy metabolism, and five transcripts are unknown or poorly characterized and have yet to be described in the nervous system. The comparison of functional gene classes indicates that the SOC has the highest energy demand of the three neural tissues, yet protein turnover is apparently not increased. This suggests a high energy demand for fueling auditory neurotransmission. Such a demand may have implications on auditory-specific tasks and relate to central auditory processing disorders. Ultimately, these data provide new avenues to foster investigations of auditory function and to advance molecular physiology in the central auditory system.

The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called 'small-world' and 'scale-free' networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain--the medial reticular formation (RF) of the brainstem--and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement.

High-Frequency Activity in Human Visual Cortex Is Modulated by Visual Motion Strength

A central goal in systems neuroscience is to understand how the brain encodes the intensity of sensory features. We used whole-head magnetoencephalography to investigate whether frequency-specific neuronal activity in the human visual cortex is systematically modulated by the intensity of an elementary sensory feature such as visual motion. Visual stimulation induced a tonic increase of neuronal activity at frequencies above 50 Hz. In order to define a functional frequency band of neuronal activity, we parametrically investigated which frequency band displays the strongest monotonic increase of responses with strength of visual motion. Consistently in all investigated subjects, this analysis resulted in a functional frequency band in the high gamma range from about 60 to 100 Hz in which activity reliably increased with visual motion strength. Using distributed source reconstruction, we found that this increase of high-frequency neuronal activity originates from several extrastriate cortical regions specialized in motion processing. We conclude that high-frequency activity in the human visual motion pathway may be relevant for encoding the intensity of visual motion signals.

Single Ih channels in pyramidal neuron dendrites: properties, distribution, and impact on action potential output

The hyperpolarization-activated cation current (Ih) plays an important role in regulating neuronal excitability, yet its native single-channel properties in the brain are essentially unknown. Here we use variance-mean analysis to study the properties of single Ih channels in the apical dendrites of cortical layer 5 pyramidal neurons in vitro. In these neurons, we find that Ih channels have an average unitary conductance of 680 +/- 30 fS (n = 18). Spectral analysis of simulated and native Ih channels showed that there is little or no channel flicker below 5 kHz. In contrast to the uniformly distributed single-channel conductance, Ih channel number increases exponentially with distance, reaching densities as high as approximately 550 channels/microm2 at distal dendritic sites. These high channel densities generate significant membrane voltage noise. By incorporating a stochastic model of Ih single-channel gating into a morphologically realistic model of a layer 5 neuron, we show that this channel noise is higher in distal dendritic compartments and increased threefold with a 10-fold increased single-channel conductance (6.8 pS) but constant Ih current density. In addition, we demonstrate that voltage fluctuations attributable to stochastic Ih channel gating impact on action potential output, with greater spike-timing precision in models with the experimentally determined single-channel conductance. These data suggest that, in the face of high current densities, the small single-channel conductance of Ih is critical for maintaining the fidelity of action potential output.

Efficient auditory coding

The auditory neural code must serve a wide range of auditory tasks that require great sensitivity in time and frequency and be effective over the diverse array of sounds present in natural acoustic environments. It has been suggested that sensory systems might have evolved highly efficient coding strategies to maximize the information conveyed to the brain while minimizing the required energy and neural resources. Here we show that, for natural sounds, the complete acoustic waveform can be represented efficiently with a nonlinear model based on a population spike code. In this model, idealized spikes encode the precise temporal positions and magnitudes of underlying acoustic features. We find that when the features are optimized for coding either natural sounds or speech, they show striking similarities to time-domain cochlear filter estimates, have a frequency-bandwidth dependence similar to that of auditory nerve fibres, and yield significantly greater coding efficiency than conventional signal representations. These results indicate that the auditory code might approach an information theoretic optimum and that the acoustic structure of speech might be adapted to the coding capacity of the mammalian auditory system.

Metabolic energy cost of action potential velocity

The action potential of the unmyelinated nerve is metabolically expensive. Using the energetic cost per unit length for the biophysically modeled action potential of the squid giant axon, we analyze this cost and identify one possible optimization. The energetic cost arising from an action potential is divided into three separate components: 1) the depolarization of the rising phase; 2) the hyperpolarization of the falling phase; and 3) the largest component, the overlapping of positive and negative currents, which has no electrical effect. Using both the Hodgkin-Huxley (HH) model and an improved version of the HH model (HHSFL), we investigate the variation of these three components as a function of easily evolvable parameters, axon diameter and ion channel densities. Assuming conduction velocity is well designed for each organism, the energy component associated with the rising phase attains a minimum near the biological values of the diameter and channel densities. This optimization is explained by the membrane capacitance per unit length. The functional capacitance is the sum of the intrinsic membrane capacitance and the gating capacitance associated with the sodium channel, and this capacitance minimizes at nearly the same values of diameter and channel density. Because capacitance is temperature independent and because this result is independent of the assumed velocity, the result generalizes to unmyelinated mammalian axons. That is, channel density is arguably an evolved property that goes hand-in-hand with the evolutionary stability of the sodium channel.

A somatotopic map of vibrissa motion direction within a barrel column

Most mammals possess high-resolution visual perception, with primary visual cortices containing fine-scale, inter-related feature representations (for example, orientation and ocular dominance). Rats lack precise vision, but their vibrissa sensory system provides a precise tactile modality, including vibrissa-related 'barrel' columns in primary somatosensory cortex. Here, we examined the subcolumnar organization of direction preference and somatotopy using a new omni-directional, multi-vibrissa stimulator. We discovered a direction map that was systematically linked to somatotopy, such that neurons were tuned for motion toward their preferred surround vibrissa. This sub-barrel column direction map demonstrated an emergent refinement from layer IV to layer II/III. These data suggest that joint processing of multiple sensory features is a common property of high-resolution sensory systems.

An optimal brain can be composed of conflicting agents

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under natural physiological limitations, an optimal decision-making system can involve "selfish" agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only.

Physical realizability of small-world networks

Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost associated with their length l, the corresponding distribution q(l) plays a crucial role. Uniform length distributions have received the most attention despite indications that q(l) approximately l(-alpha) exists-e.g., for integrated circuits, the Internet, and cortical networks. While length distributions of this type were previously examined in the context of navigability, we here discuss for such systems the emergence and physical realizability of small-world topology. Our simple argument allows us to understand under which condition and at what expense a small world results.

Learning by message passing in networks of discrete synapses

We show that a message-passing process allows us to store in binary "material" synapses a number of random patterns which almost saturate the information theoretic bounds. We apply the learning algorithm to networks characterized by a wide range of different connection topologies and of size comparable with that of biological systems (e.g., [EQUATION: SEE TEXT]). The algorithm can be turned into an online-fault tolerant-learning protocol of potential interest in modeling aspects of synaptic plasticity and in building neuromorphic devices.

A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs

Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03-0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.

Segregation of the brain into gray and white matter: a design minimizing conduction delays

A ubiquitous feature of the vertebrate anatomy is the segregation of the brain into white and gray matter. Assuming that evolution maximized brain functionality, what is the reason for such segregation? To answer this question, we posit that brain functionality requires high interconnectivity and short conduction delays. Based on this assumption we searched for the optimal brain architecture by comparing different candidate designs. We found that the optimal design depends on the number of neurons, interneuronal connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into white and gray matter. These results provide a possible explanation for the structure of various regions of the vertebrate brain, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord.

Neuroenergetics and the kinetic design of excitatory synapses

Why is the characteristic timescale of neural information processing in the millisecond range, corresponding to a 'clock speed' of about 1 kHz, whereas the clock speed of modern computers is about 3 GHz? Here we investigate how the brain's energy supply limits the maximum rate at which the brain can compute, and how the molecular components of excitatory synapses have evolved properties that are matched to the information processing they perform.

Being a self: considerations from functional imaging

Having a self is associated with important advantages for an organism. These advantages have been suggested to include mechanisms supporting elaborate capacities for planning, decision-making, and behavioral control. Acknowledging such functionality offers possibilities for obtaining traction on investigation of neural correlates of self-hood. A method that has potential for investigating some of the brain-based properties of self arising in behavioral contexts varying in requirements for such behavioral guidance and control is functional brain imaging. Data obtained with this method are beginning to converge on a set of brain areas that appear to play a significant role in permitting conscious access to representational content having reference to self as an embodied and independent experiencer and agent. These areas have been identified in a variety of imaging contexts ranging from passive state conditions in which they appear to manifest ongoing activity associated with spontaneous and typically 'self-related' cognition, to tasks targeting explicitly experienced properties of self, to demanding task conditions where activity within them is attenuated in apparent redirection of cognitive resources in the service of task guidance and control. In this paper, these data will be reviewed and a hypothesis presented regarding a significant role for these areas in enabling degrees of self-awareness and participating in the management of such behavioral control.

Systems biology approaches in cell signaling research

The use of methods for global and quantitative analysis of cells is providing new systems-level insights into signal transduction processes. Recent studies reveal important information about the rates of signal transmission and propagation, help establish some general regulatory characteristics of multi-tiered signaling cascades, and illuminate the combinatorial nature of signaling specificity in cell differentiation.

Physiological and pathological changes in glucose regulate brain Akt and glycogen synthase kinase-3

Insulin regulates the phosphorylation and activities of Akt and glycogen synthase kinase-3 (GSK3) in peripheral tissues, but in the brain it is less clear how this signaling pathway is regulated in vivo and whether it is affected by diabetes. We found that Akt and GSK3 are sensitive to glucose, because fasting decreased and glucose administration increased by severalfold the phosphorylation of Akt and GSK3 in the cerebral cortex and hippocampus of non-diabetic mice. Brain Akt and GSK3 phosphorylation also increased after streptozotocin administration (3 days), which increased blood glucose and depleted blood insulin, indicating regulation by glucose availability even with deficient insulin. Changes in Akt and GSK3 phosphorylation and activities in epididymal fat were opposite to those of brain after streptozotocin treatment. Streptozotocin-induced hyperglycemia and increased brain Akt and GSK3 phosphorylation were reversed by lowering blood glucose with insulin administration. Long term hyperglycemia also increased brain Akt and GSK3 phosphorylation, both 4 weeks after streptozotocin and in db/db insulin-resistant mice. Thus, the Akt-GSK3 signaling pathway is regulated in mouse brain in vivo in response to physiological and pathological changes in insulin and glucose.

Implicit exploitation of regularities: novel correlations in images quickly alter visual perception

Viewing a set of two thousand images in which the contrasts of a central and a surrounding pattern were highly correlated increased the suppressive influence of the surround on the perceived contrast of the central pattern. The apparent increase in inhibition supports the operation of an anti-Hebbian mechanism between the two groups of cells excited by the patterns (one group by the central pattern and the other by the surround). According to this mechanism, inhibitory connections between nearby cells increase in efficacy according to a simple function of the correlations between the cells' activities.

THE PLASTIC HUMAN BRAIN CORTEX

Plasticity is an intrinsic property of the human brain and represents evolution's invention to enable the nervous system to escape the restrictions of its own genome and thus adapt to environmental pressures, physiologic changes, and experiences. Dynamic shifts in the strength of preexisting connections across distributed neural networks, changes in task-related cortico-cortical and cortico-subcortical coherence and modifications of the mapping between behavior and neural activity take place in response to changes in afferent input or efferent demand. Such rapid, ongoing changes may be followed by the establishment of new connections through dendritic growth and arborization. However, they harbor the danger that the evolving pattern of neural activation may in itself lead to abnormal behavior. Plasticity is the mechanism for development and learning, as much as a cause of pathology. The challenge we face is to learn enough about the mechanisms of plasticity to modulate them to achieve the best behavioral outcome for a given subject.

Diffusion processes on power-law small-world networks

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The results were obtained using self-consistent perturbation theory and can also be understood in terms of a scaling theory, which provides a general framework for understanding processes on small-world networks with different distributions of long-range links.

Is the early visual system optimised to be energy efficient?

This paper demonstrates that a representation which balances natural image encoding with metabolic energy efficiency shows many similarities to the neural organisation observed in the early visual system. A simple linear model was constructed that learned receptive fields by optimally balancing information coding with metabolic expense for an entire visual field in a 2-stage visual system. The input to the model consists of a space variant retinal array of photoreceptors. Natural images were then encoded through a bottleneck such as the retinal ganglion cells that form the optic nerve. The natural images represented by the activity of retinal ganglion cells were then encoded by many more 'cortical' cells in a divergent representation. Qualitatively, the system learnt by optimising information coding and energy expenditure and matched (1) the centre surround organisation of retinal ganglion cells; (2) the Gabor-like organisation of cortical simple cells; (3) higher densities of receptive fields in the fovea decreasing in the periphery; (4) smaller receptive fields in the fovea increasing in size in the periphery; (5) spacing ratios of retinal cells; and (6) aspect ratios of cortical receptive fields. Quantitatively, however, there are small but significant discrepancies between density slopes which may be accounted for by taking optic blur and fixation induced image statistics into account. In addition, the model cortical receptive fields are more broadly tuned than biological cortical neurons; this may be accounted for by the computational limitation of modelling a relatively low number of neurons. This paper shows that retinal receptive field properties can be understood in terms of balancing coding with synaptic energy expenditure and cortical receptive fields with firing rate energy expenditure, and provides a sound biological explanation of why 'sparse' distributions are beneficial.

Normal and pathological oscillatory communication in the brain

The huge number of neurons in the human brain are connected to form functionally specialized assemblies. The brain's amazing processing capabilities rest on local communication within and long-range communication between these assemblies. Even simple sensory, motor and cognitive tasks depend on the precise coordination of many brain areas. Recent improvements in the methods of studying long-range communication have allowed us to address several important questions. What are the common mechanisms that govern local and long-range communication and how do they relate to the structure of the brain? How does oscillatory synchronization subserve neural communication? And what are the consequences of abnormal synchronization?

Selectivity and sparseness in the responses of striate complex cells

Probability distributions of macaque complex cell responses to a large set of images were determined. Measures of selectivity were based on the overall shape of the response probability distribution, as quantified by either kurtosis or entropy. We call this non-parametric selectivity, in contrast to parametric selectivity, which measures tuning curve bandwidths. To examine how receptive field properties affected non-parametric selectivity, two models of complex cells were created. One was a standard Gabor energy model, and the other a slight variant constructed from a Gabor function and its Hilbert transform. Functionally, these models differed primarily in the size of their DC responses. The Hilbert model produced higher selectivities than the Gabor model, with the two models bracketing the data from above and below. Thus we see that tiny changes in the receptive field profiles can lead to major changes in selectivity. While selectivity looks at the response distribution of a single neuron across a set of stimuli, sparseness looks at the response distribution of a population of neurons to a single stimulus. In the model, we found that on average the sparseness of a population was equal to the selectivity of cells comprising that population, a property we call ergodicity. We raise the possibility that high sparseness is the result of distortions in the shape of response distributions caused by non-linear, information-losing transforms, unrelated to information theoretic issues of efficient coding.

Noise-enhanced categorization in a recurrently reconnected neural network

We investigate the interplay of recurrence and noise in neural networks trained to categorize spatial patterns of neural activity. We develop the following procedure to demonstrate how, in the presence of noise, the introduction of recurrence permits to significantly extend and homogenize the operating range of a feed-forward neural network. We first train a two-level perceptron in the absence of noise. Following training, we identify the input and output units of the feed-forward network, and thus convert it into a two-layer recurrent network. We show that the performance of the reconnected network has features reminiscent of nondynamic stochastic resonance: the addition of noise enables the network to correctly categorize stimuli of subthreshold strength, with optimal noise magnitude significantly exceeding the stimulus strength. We characterize the dynamics leading to this effect and contrast it to the behavior of a more simple associative memory network in which noise-mediated categorization fails.