Effect of the topology and delayed interactions in neuronal networks synchronization

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.     

Basic mechanisms for graded persistent activity: discrete attractors,continuous attractors,and dynamic representations

Persistent neural activity is observed in many systems, and is thought to be a neural substrate for holding memories over time delays of a few seconds. Recent work has addressed two issues. First, how can networks of neurons robustly hold such an active memory? Computer systems obtain significant robustness to noise by approximating analogue quantities with discrete digital representations. In a similar manner, theoretical models of persistent activity in spiking neurons have shown that the most robust and stable way to store the short-term memory of a continuous parameter is to approximate it with a discrete representation. This general idea applies very broadly to mechanisms that range from biochemical networks to single cells and to large circuits of neurons. Second, why is it commonly observed that persistent activity in the cortex can be strongly time-varying? This observation is almost ubiquitous, and therefore must be taken into account in our models and our understanding of how short-term memories are held in the cortex.     

Weak electric fields detectability in a noisy neural network

We investigate the detectability of weak electric field in a noisy neural network based on Izhikevich neuron model systematically. The neural network is composed of excitatory and inhibitory neurons with similar ratio as that in the mammalian neocortex, and the axonal conduction delays between neurons are also considered. It is found that the noise intensity can modulate the detectability of weak electric field. Stochastic resonance (SR) phenomenon induced by white noise is observed when the weak electric field is added to the network. It is interesting that SR almost disappeared when the connections between neurons are cancelled, suggesting the amplification effects of the neural coupling on the synchronization of neuronal spiking. Furthermore, the network parameters, such as the connection probability, the synaptic coupling strength, the scale of neuron population and the neuron heterogeneity, can also affect the detectability of the weak electric field. Finally, the model sensitivity is studied in detail, and results show that the neural network model has an optimal region for the detectability of weak electric field signal.     

Vibrational resonance in a randomly connected neural network

A randomly connected network is constructed with similar characteristics (e.g., the ratio of excitatory and inhibitory neurons, the connection probability between neurons, and the axonal conduction delays) as that in the mammalian neocortex and the effects of high-frequency electrical field on the response of the network to a subthreshold low-frequency electrical field are studied in detail. It is found that both the amplitude and frequency of the high-frequency electrical field can modulate the response of the network to the low-frequency electric field. Moreover, vibrational resonance (VR) phenomenon induced by the two types of electrical fields can also be influenced by the network parameters, such as the neuron population, the connection probability between neurons and the synaptic strength. It is interesting that VR is found to be related with the ratio of excitatory neurons that are under high-frequency electrical stimuli. In summary, it is suggested that the interaction of excitatory and inhibitory currents is also an important factor that can influence the performance of VR in neural networks.     

Population density models of integrate-and-fire neurons with jumps: well-posedness

In this paper we study the well-posedness of different models of population of leaky integrate-and-fire neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the different behaviours of the model with jumps compared to its diffusion approximation.     

F3/contactin,a neuronal cell adhesion molecule implicated in axogenesis and myelination

A general feature of the cell adhesion molecules belonging to the immunoglobulin family (Ig-CAMs) is to display a modular structure that provides a framework for multiple binding sites for other recognition molecules. Among this family, F3/contactin is a glycan phosphatidyl-inositol (GPI)-anchored molecule expressed by neurons that displays the distinctiveness to exert heterophilic but no homophilic binding activities. The Ig domains of F3/contactin were shown to interact with the L1 family of Ig-CAMs, including L1, NrCAM, and neurofascin. Binding between F3/contactin and NrCAM is known to modulate axonal elongation of the cerebellar granule cells and to control sensory axon guidance. F3/contactin mediates neuron-glial contacts through its association with extracellular matrix components (tenascin-R, tenascin-C) and RPTPbeta/phosphacan, influencing axonal growth and fasciculation. Another major role of F3/contactin is to organize axonal subdomains at the node of Ranvier of myelinated fibers in interplay with other Ig-CAMs, through its binding with caspr/paranodin at paranodes and the voltage-gated sodium channels in the nodal region. The F3/contactin deficient mice display a severe ataxia correlated with defects in axonal and dendritic projections in the cerebellum. These mice also display defects in nerve influx conduction due to the disruption of the axo-glial contacts at paranodes. Finally, the recent identification of a Drosophila homologue of F3/contactin indicated that this family of GPI-anchored CAMs plays a conserved function in axonal insulation.     

Multiple forms of activity-dependent competition refine hippocampal circuits in vivo

Efficient memory formation relies on the establishment of functional hippocampal circuits. It has been proposed that synaptic connections are refined by neural activity to form functional brain circuitry. However, it is not known whether and how hippocampal connections are refined by neural activity in vivo. Using a mouse genetic system in which restricted populations of neurons in the hippocampal circuit are inactivated, we show that inactive axons are eliminated after they develop through a competition with active axons. Remarkably, in the dentate gyrus, which undergoes neurogenesis throughout life, axon refinement is achieved by a competition between mature and young neurons. These results demonstrate that activity-dependent competition plays multiple roles in the establishment of functional memory circuits in vivo.     

Spiking neural network simulation: memory-optimal synaptic event scheduling

Spiking neural network simulations incorporating variable transmission delays require synaptic events to be scheduled prior to delivery. Conventional methods have memory requirements that scale with the total number of synapses in a network. We introduce novel scheduling algorithms for both discrete and continuous event delivery, where the memory requirement scales instead with the number of neurons. Superior algorithmic performance is demonstrated using large-scale, benchmarking network simulations.     

具有竞争指针的短时记忆神经网络模型

在我们以前提出的短时记忆神经网络模型基础上［３］,我们在新模型中引入突触竞争机制,提出了一个新的短时记忆神经网络模型。模型仍由两个神经网络所组成;其一为与长时记忆共有的信息内容表达网络,另一个为指针神经元环路。由于表达区神经元与指针神经元间的突触权重的竞争,使得模型可以表现出由干扰引起的短时记忆的遗忘。相应于自由回忆序列位置效应和汉字组块两个心理学实验,对模型做了计算机仿真。仿真结果显示模型的行为与两个心理实验定量地符合得很好。由此表明现在的模型更合适于作为短时记忆的模型。     

Visual inter-hemispheric processing: constraints and potentialities set by axonal morphology.

The largest bundle of axonal fibers in the entire mammalian brain, namely the corpus callosum, is the pathway through which almost half a billion neurons scattered over all neocortical areas can exert an influence on their contralateral targets. These fibers are thus crucial participants in the numerous cortical functions requiring collaborative processing of information across the hemispheres. One of such operations is to combine the two partial cortical maps of the visual field into a single, coherent representation. This paper reviews recent anatomical, computational and electrophysiological studies on callosal connectivity in the cat visual system. We analyzed the morphology of individual callosal axons linking primary visual cortices using three-dimensional light-microscopic techniques. While only a minority of callosal axons seem to perform a strict 'point-to-point' mapping between retinotopically corresponding sites in both hemispheres, many others have widespread arbors and terminate into a handful of distant, radially oriented tufts. Therefore, the firing of a single callosal neuron might influence several cortical columns within the opposite hemisphere. Computer simulation was then applied to investigate how the intricate geometry of these axons might shape the spatio-temporal distribution of trans-callosal inputs. Based on the linear relation between diameter and conduction velocity of myelinated fibers, the theoretical delays required for a single action potential to reach all presynaptic boutons of a given arbor were derived from the caliber, g-ratio and length of successive axonal segments. This analysis suggests that the architecture of callosal axons is, in principle, suitable to promote the synchronous activation of multiple targets located across distant columns in the opposite hemisphere. Finally, electrophysiological recordings performed in several laboratories have shown the existence of stimulus-dependent synchronization of visual responses across the two hemispheres. Possible implications of these findings are discussed in the context of temporal tagging of neuronal assemblies.     

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

 We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons with synaptic coupling. This provides a simple model of excitable neural tissue. We first derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-propagation depends on various parameters that characterize neuronal interactions such as synaptic and axonal delays, and the passive membrane properties of dendritic cables. We also establish that excitable networks support the propagation of solitary pulses in the long-wavelength limit. We then derive a general condition for the (local) asymptotic stability of traveling waves in terms of the characteristic equation of the linearized firing time map, which takes the form of an integro-difference equation of infinite order. We use this to analyze the stability of solitary pulses in the long-wavelength limit. Solitary wave solutions are shown to come in pairs with the faster (slower) solution stable (unstable) in the case of zero axonal delays; for non-zero delays and fast synapses the stable wave can itself destabilize via a Hopf bifurcation. Received: 27 October 1998     

Forced expression of Phox2 homeodomain transcription factors induces a branchio-visceromotor axonal phenotype

What causes motor neurons to project into the periphery is not well understood. We here show that forced expression of the homeodomain protein Phox2b, shown previously to be necessary and sufficient for branchio-visceromotor neuron development, and of its paralogue Phox2a imposes a branchiomotor-like axonal phenotype in the spinal cord. Many Phox2-transfected neurons, whose axons would normally stay within the confines of the neural tube, now project into the periphery. Once outside the neural tube, a fraction of the ectopic axons join the spinal accessory nerve, a branchiomotor nerve which, as shown here, does not develop in the absence of Phox2b. Explant studies show that the axons of Phox2-transfected neurons need attractive cues to leave the neural tube and that their outgrowth is promoted by tissues, to which branchio-visceromotor fibers normally grow. Hence, Phox2 expression is a key step in determining the peripheral axonal phenotype and thus the decision to stay within the neural tube or to project out of it.     

Longitudinal coordination of motor output during swimming in Xenopus embryos.

Little is known about the neural mechanisms that control the phenomenon of rostro-caudal delay. In Xenopus embryos there is a constant rostro-caudal delay of 2-5 ms mm-1 during fictive swimming. Rostro-caudal delay is not significantly correlated with cycle period. When NMDA is applied to the caudal spinal cord there is a decrease and in some cases a reversal in rostro-caudal delay. Conversely applying excitatory antagonists to the caudal spinal cord leads to an increase in delay. When caudal mid-cycle inhibition is reduced either pharmacologically using strychnine or surgically through hemisection of the spinal cord, there is an increase in rostro-caudal delay. Rostro-caudal delays are too small to be explainable on the basis of axonal conduction velocities and synaptic delays. This suggests that the central pattern generator of Xenopus behaves as a series of coupled oscillators and that the nature of the coupling, together with a longitudinal gradient in excitability associated with the oscillators, contributes to the observed rostro-caudal delay.     

Ephaptic coupling in white matter fibre bundles modulates axonal transmission delays

Axonal connections are widely regarded as faithful transmitters of neuronal signals with fixed delays. The reasoning behind this is that extracellular potentials caused by spikes travelling along axons are too small to have an effect on other axons. Here we devise a computational framework that allows us to study the effect of extracellular potentials generated by spike volleys in axonal fibre bundles on axonal transmission delays. We demonstrate that, although the extracellular potentials generated by single spikes are of the order of microvolts, the collective extracellular potential generated by spike volleys can reach several millivolts. As a consequence, the resulting depolarisation of the axonal membranes increases the velocity of spikes, and therefore reduces axonal delays between brain areas. Driving a neural mass model with such spike volleys, we further demonstrate that only ephaptic coupling can explain the reduction of stimulus latencies with increased stimulus intensities, as observed in many psychological experiments.     

Ephrin reverse signaling in axon guidance and synaptogenesis

Axon-cell and axon-dendrite contact is a highly regulated process necessary for the formation of precise neural circuits and a functional neural network. Eph-ephrin interacting molecules on the membranes of axon nerve terminals and target dendrites act as bidirectional ligands/receptors to transduce signals into both the Eph-expressing and ephrin-expressing cells to regulate cytoskeletal dynamics. In particular, recent evidence indicates that ephrin reverse signal transduction events are important in controlling both axonal and dendritic elaborations of neurons in the developing nervous system. Here we review how ephrin reverse signals are transduced into neurons to control maturation of axonal pre-synaptic and dendritic post-synaptic structures.     

Axonal transmission in the retina introduces a small dispersion of relative timing in the ganglion cell population response

Background

Visual stimuli elicit action potentials in tens of different retinal ganglion cells. Each ganglion cell type responds with a different latency to a given stimulus, thus transforming the high-dimensional input into a temporal neural code. The timing of the first spikes between different retinal projection neurons cells may further change along axonal transmission. The purpose of this study is to investigate if intraretinal conduction velocity leads to a synchronization or dispersion of the population signal leaving the eye.

Methodology/Principal Findings

We ‘imaged’ the initiation and transmission of light-evoked action potentials along individual axons in the rabbit retina at micron-scale resolution using a high-density multi-transistor array. We measured unimodal conduction velocity distributions (1.3±0.3 m/sec, mean ± SD) for axonal populations at all retinal eccentricities with the exception of the central part that contains myelinated axons. The velocity variance within each piece of retina is caused by ganglion cell types that show narrower and slightly different average velocity tuning. Ganglion cells of the same type respond with similar latency to spatially homogenous stimuli and conduct with similar velocity. For ganglion cells of different type intraretinal conduction velocity and response latency to flashed stimuli are negatively correlated, indicating that differences in first spike timing increase (up to 10 msec). Similarly, the analysis of pair-wise correlated activity in response to white-noise stimuli reveals that conduction velocity and response latency are negatively correlated.

Conclusion/Significance

Intraretinal conduction does not change the relative spike timing between ganglion cells of the same type but increases spike timing differences among ganglion cells of different type. The fastest retinal ganglion cells therefore act as indicators of new stimuli for postsynaptic neurons. The intraretinal dispersion of the population activity will not be compensated by variability in extraretinal conduction times, estimated from data in the literature.     

Short-term environmental enrichment rescues adult neurogenesis and memory deficits in APP(Sw,Ind) transgenic mice

Epidemiological studies indicate that intellectual activity prevents or delays the onset of Alzheimer's disease (AD). Similarly, cognitive stimulation using environmental enrichment (EE), which increases adult neurogenesis and functional integration of newborn neurons into neural circuits of the hippocampus, protects against memory decline in transgenic mouse models of AD, but the mechanisms involved are poorly understood. To study the therapeutic benefits of cognitive stimulation in AD we examined the effects of EE in hippocampal neurogenesis and memory in a transgenic mouse model of AD expressing the human mutant β-amyloid (Aβ) precursor protein (APP(Sw,Ind)). By using molecular markers of new generated neurons (bromodeoxiuridine, NeuN and doublecortin), we found reduced neurogenesis and decreased dendritic length and projections of doublecortin-expressing cells of the dentate gyrus in young APP(Sw,Ind) transgenic mice. Moreover, we detected a lower number of mature neurons (NeuN positive) in the granular cell layer and a reduced volume of the dentate gyrus that could be due to a sustained decrease in the incorporation of new generated neurons. We found that short-term EE for 7 weeks efficiently ameliorates early hippocampal-dependent spatial learning and memory deficits in APP(Sw,Ind) transgenic mice. The cognitive benefits of enrichment in APP(Sw,Ind) transgenic mice were associated with increased number, dendritic length and projections to the CA3 region of the most mature adult newborn neurons. By contrast, Aβ levels and the total number of neurons in the dentate gyrus were unchanged by EE in APP(Sw,Ind) mice. These results suggest that promoting the survival and maturation of adult generated newborn neurons in the hippocampus may contribute to cognitive benefits in AD mouse models.     

Is bigger always better? A critical appraisal of the use of volumetric analysis in the study of the hippocampus

A well-developed spatial memory is important for many animals, but appears especially important for scatter-hoarding species. Consequently, the scatter-hoarding system provides an excellent paradigm in which to study the integrative aspects of memory use within an ecological and evolutionary framework. One of the main tenets of this paradigm is that selection for enhanced spatial memory for cache locations should specialize the brain areas involved in memory. One such brain area is the hippocampus (Hp). Many studies have examined this adaptive specialization hypothesis, typically relating spatial memory to Hp volume. However, it is unclear how the volume of the Hp is related to its function for spatial memory. Thus, the goal of this article is to evaluate volume as a main measurement of the degree of morphological and physiological adaptation of the Hp as it relates to memory. We will briefly review the evidence for the specialization of memory in food-hoarding animals and discuss the philosophy behind volume as the main currency. We will then examine the problems associated with this approach, attempting to understand the advantages and limitations of using volume and discuss alternatives that might yield more specific hypotheses. Overall, there is strong evidence that the Hp is involved in the specialization of spatial memory in scatter-hoarding animals. However, volume may be only a coarse proxy for more relevant and subtle changes in the structure of the brain underlying changes in behaviour. To better understand the nature of this brain/memory relationship, we suggest focusing on more specific and relevant features of the Hp, such as the number or size of neurons, variation in connectivity depending on dendritic and axonal arborization and the number of synapses. These should generate more specific hypotheses derived from a solid theoretical background and should provide a better understanding of both neural mechanisms of memory and their evolution.     

Axonal conduction and injury in multiple sclerosis: the role of sodium channels

Multiple sclerosis (MS) is the most common cause of neurological disability in young adults. Recent studies have implicated specific sodium channel isoforms as having an important role in several aspects of the pathophysiology of MS, including the restoration of impulse conduction after demyelination, axonal degeneration and the mistuning of Purkinje neurons that leads to cerebellar dysfunction. By manipulating the activity of these channels or their expression, it might be possible to develop new therapeutic approaches that will prevent or limit disability in MS.     

Addition of new neurons and the emergence of a local neural circuit for precise timing

During development, neurons arrive at local brain areas in an extended period of time, but how they form local neural circuits is unknown. Here we computationally model the emergence of a network for precise timing in the premotor nucleus HVC in songbird. We show that new projection neurons, added to HVC post hatch at early stages of song development, are recruited to the end of a growing feedforward network. High spontaneous activity of the new neurons makes them the prime targets for recruitment in a self-organized process via synaptic plasticity. Once recruited, the new neurons fire readily at precise times, and they become mature. Neurons that are not recruited become silent and replaced by new immature neurons. Our model incorporates realistic HVC features such as interneurons, spatial distributions of neurons, and distributed axonal delays. The model predicts that the birth order of the projection neurons correlates with their burst timing during the song.