Long term memory storage capacity of multiconnected neural networks

Quantitative expressions of long-term memory storage capacities of complex neural network are derived. The networks are made of neurons connected by synapses of any order, of the axono-axonal type considered by Kandel et al. for example. The effect of link deletion possibly related to aging, is also considered. The central result of this study is that, within the framework of Hebb's laws, the number of stored bits is proportional to the number of synapses. The proportionality factor however, decreases when the order of involved synaptic contact increases. This tends to favor neural architectures with low-order synaptic connectivities. It is finally shown that the memory storage capacities can be optimized by a partition of the network into neuron clusters with size comparable with that observed for cortical microcolumns.     

Contactin-associated protein 1 (Caspr1) regulates the traffic and synaptic content of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)-type glutamate receptors

Glutamate receptors of the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) type mediate fast excitatory synaptic transmission in the CNS. Synaptic strength is modulated by AMPA receptor binding partners, which regulate receptor synaptic targeting and functional properties. We identify Contactin-associated protein 1 (Caspr1) as an AMPA receptor interactor. Caspr1 is present in synapses and interacts with AMPA receptors in brain synaptic fractions. Coexpression of Caspr1 with GluA1 increases the amplitude of glutamate-evoked currents. Caspr1 overexpression in hippocampal neurons increases the number and size of synaptic GluA1 clusters, whereas knockdown of Caspr1 decreases the intensity of synaptic GluA1 clusters. Hence, Caspr1 is a regulator of the trafficking of AMPA receptors to synapses.     

Multiple association states between glycine receptors and gephyrin identified by SPT analysis

The scaffolding protein gephyrin is known to anchor glycine receptors (GlyR) at synapses and to participate in the dynamic equilibrium between synaptic and extrasynaptic GlyR in the neuronal membrane. Here we investigated the properties of this interaction in cells cotransfected with YFP-tagged gephyrin and GlyR subunits possessing an extracellular myc-tag. In HeLa cells and young neurons, single particle tracking was used to follow in real time individual GlyR, labeled with quantum dots, traveling into and out of gephyrin clusters. Analysis of the diffusion properties of two GlyR subunit types--able or unable to bind gephyrin--gave access to the association states of GlyR with its scaffolding protein. Our results indicated that an important portion of GlyR could be linked to a few molecules of gephyrin outside gephyrin clusters. This emphasizes the role of scaffolding proteins in the extrasynaptic membrane and supports the implication of gephyrin-gephyrin interactions in the stabilization of GlyR at synapses. The kinetic parameters controlling the equilibrium between GlyR inside and outside clusters were also characterized. Within clusters, we identified two subpopulations of GlyR with distinct degrees of stabilization between receptors and scaffolding proteins.     

Long-Term Relationships between Synaptic Tenacity, Synaptic Remodeling, and Network Activity

Synaptic plasticity is widely believed to constitute a key mechanism for modifying functional properties of neuronal networks. This belief implicitly implies, however, that synapses, when not driven to change their characteristics by physiologically relevant stimuli, will maintain these characteristics over time. How tenacious are synapses over behaviorally relevant time scales? To begin to address this question, we developed a system for continuously imaging the structural dynamics of individual synapses over many days, while recording network activity in the same preparations. We found that in spontaneously active networks, distributions of synaptic sizes were generally stable over days. Following individual synapses revealed, however, that the apparently static distributions were actually steady states of synapses exhibiting continual and extensive remodeling. In active networks, large synapses tended to grow smaller, whereas small synapses tended to grow larger, mainly during periods of particularly synchronous activity. Suppression of network activity only mildly affected the magnitude of synaptic remodeling, but dependence on synaptic size was lost, leading to the broadening of synaptic size distributions and increases in mean synaptic size. From the perspective of individual neurons, activity drove changes in the relative sizes of their excitatory inputs, but such changes continued, albeit at lower rates, even when network activity was blocked. Our findings show that activity strongly drives synaptic remodeling, but they also show that significant remodeling occurs spontaneously. Whereas such spontaneous remodeling provides an explanation for “synaptic homeostasis” like processes, it also raises significant questions concerning the reliability of individual synapses as sites for persistently modifying network function.     

Self-similarity properties of alpha-crystallin supramolecular aggregates.

The supramolecular aggregation of alpha-crystallin, the major protein of the eye lens, was investigated by means of static and dynamic light scattering. The aggregation was induced by generating heat-modified alpha-crystallin forms and by stabilizing the clusters with calcium ions. The kinetic pattern of the aggregation and the structural features of the clusters can be described according to the reaction limited cluster-cluster aggregation theory previously adopted for the study of colloidal particles aggregation systems. Accordingly, the average mass and the hydrodynamic radius of alpha-crystallin supramolecular aggregates grow exponentially in time. The structure factor of the clusters is typical of fractal aggregates. A fractal dimension df approximately 2.15 was determined, indicating a low probability of sticking together of the primitive aggregating particles. As a consequence, the slow-forming clusters assemble a rather compact structure. The basic units forming the fractal aggregates were found to have a radius about twice (approximately 17 nm) that of the native protein and 5.3 times its size, which is consistent with an intermediate molecular assembly corresponding to the already known high molecular weight forms of alpha-crystallin.     

Dynamics of pruning in simulated large-scale spiking neural networks

Massive synaptic pruning following over-growth is a general feature of mammalian brain maturation. This article studies the synaptic pruning that occurs in large networks of simulated spiking neurons in the absence of specific input patterns of activity. The evolution of connections between neurons were governed by an original bioinspired spike-timing-dependent synaptic plasticity (STDP) modification rule which included a slow decay term. The network reached a steady state with a bimodal distribution of the synaptic weights that were either incremented to the maximum value or decremented to the lowest value. After 1x10(6) time steps the final number of synapses that remained active was below 10% of the number of initially active synapses independently of network size. The synaptic modification rule did not introduce spurious biases in the geometrical distribution of the remaining active projections. The results show that, under certain conditions, the model is capable of generating spontaneously emergent cell assemblies.     

Rapid redistribution of synaptic PSD-95 in the neocortex in vivo

Most excitatory synapses terminate on dendritic spines. Spines vary in size, and their volumes are proportional to the area of the postsynaptic density (PSD) and synaptic strength. PSD-95 is an abundant multi-domain postsynaptic scaffolding protein that clusters glutamate receptors and organizes the associated signaling complexes. PSD-95 is thought to determine the size and strength of synapses. Although spines and their synapses can persist for months in vivo, PSD-95 and other PSD proteins have shorter half-lives in vitro, on the order of hours. To probe the mechanisms underlying synapse stability, we measured the dynamics of synaptic PSD-95 clusters in vivo. Using two-photon microscopy, we imaged PSD-95 tagged with GFP in layer 2/3 dendrites in the developing (postnatal day 10–21) barrel cortex. A subset of PSD-95 clusters was stable for days. Using two-photon photoactivation of PSD-95 tagged with photoactivatable GFP (paGFP), we measured the time over which PSD-95 molecules were retained in individual spines. Synaptic PSD-95 turned over rapidly (median retention times τ_r ~ 22–63 min from P10–P21) and exchanged with PSD-95 in neighboring spines by diffusion. PSDs therefore share a dynamic pool of PSD-95. Large PSDs in large spines captured more diffusing PSD-95 and also retained PSD-95 longer than small PSDs. Changes in the sizes of individual PSDs over days were associated with concomitant changes in PSD-95 retention times. Furthermore, retention times increased with developmental age (τ_r ~ 100 min at postnatal day 70) and decreased dramatically following sensory deprivation. Our data suggest that individual PSDs compete for PSD-95 and that the kinetic interactions between PSD molecules and PSDs are tuned to regulate PSD size.     

Towards eliminating bias in cluster analysis of TB genotyped data

The relative contributions of transmission and reactivation of latent infection to TB cases observed clinically has been reported in many situations, but always with some uncertainty. Genotyped data from TB organisms obtained from patients have been used as the basis for heuristic distinctions between circulating (clustered strains) and reactivated infections (unclustered strains). Naïve methods previously applied to the analysis of such data are known to provide biased estimates of the proportion of unclustered cases. The hypergeometric distribution, which generates probabilities of observing clusters of a given size as realized clusters of all possible sizes, is analyzed in this paper to yield a formal estimator for genotype cluster sizes. Subtle aspects of numerical stability, bias, and variance are explored. This formal estimator is seen to be stable with respect to the epidemiologically interesting properties of the cluster size distribution (the number of clusters and the number of singletons) though it does not yield satisfactory estimates of the number of clusters of larger sizes. The problem that even complete coverage of genotyping, in a practical sampling frame, will only provide a partial view of the actual transmission network remains to be explored.     

On the stationary state of a network of inhibitory spiking neurons

The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. For the case of fast synapses, numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately – on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short time periods. The firing rate increases linearly with external stimuli. In the limit of infinitely large networks, the synaptic noise decreases to zero. Nevertheless, the distribution of interspike intervals remains broad. Action Editor: Misha Tsodyks     

Immunocytochemical identification of synaptotagmin 1, syntaxin 1, Ca2+ channel of the N-type, and nicotinic cholinoreceptor in motor neuromuscular junctions of somatic muscle of the earthworm Lumbricus terrestris

The earthworm somatic muscle contains myoneural synapses forming clusters of “synaptic buttons” in which the proteins syntaxin 1, synaptotagmin 1, and alpha 1B subunit of the Ca²⁺ channel of the N-type were identified. It is supposed that “synaptic buttons” contain a limited number of active zones, which is due to their small size (1–2 μm) and the pattern of distribution of proteins of the exoendocytotic cycle. The postsynaptic membrane of cholinergic synapses contains nicotinic acetylcholine receptors able to bind alpha-bungarotoxin. The area of the position of receptors on postsynaptic membrane is strongly restricted to the synaptic contact region.     

The Receptor Tyrosine Kinase Met and Its Ligand Hepatocyte Growth Factor are Clustered at Excitatory Synapses and Can Enhance Clustering of Synaptic Proteins

The receptor protein tyrosine kinase Met and its ligand, hepatocyte growth factor, regulate cellular morphology, intercellular adhesion, and interactions among junctional proteins in numerous cell types. However, they have not been extensively studied in the central nervous system. We report that Met is clustered at excitatory synapses and that treatment of neurons with hepatocyte growth factor can enhance expression and clustering of synaptic proteins. We demonstrate that Met is present in clusters that strongly colocalize with the NR2B subunit of the N-methyl-D-aspartate receptor, PSD-95, and synapsin at excitatory synapses on hippocampal neurons in vitro. We also show that Met is clustered at the postsynaptic density of excitatory synapses in the CA1 region of the hippocampus with the use of immuno-electron microscopy. Hepatocyte growth factor also forms clusters that partially colocalize with PSD-95. Treatment of cultured neurons with exogenous hepatocyte growth factor increased expression of the NR2B subunit of the N-methyl-D-aspartate receptor, calcium/calmodulin-dependent protein kinase II, and the GluR1 subunit of the alpha-amino-3-hydroxy-5-methylisoxazole-4-propionate receptor. The size and number of clusters of these proteins were also increased at sites along dendrites in response to hepatocyte growth factor. These results suggest a novel role for Met and hepatocyte growth factor in regulating synapses.     

Probabilistic secretion of quanta in the central nervous system: granule cell synaptic control of pattern separation and activity regulation.

The implications of probabilistic secretion of quanta for the functioning of neural networks in the central nervous system have been explored. A model of stochastic secretion at synapses in simple networks, consisting of large numbers of granule cells and a relatively small number of inhibitory interneurons, has been analysed. Such networks occur in the input to the cerebellum Purkinje cells as well as to hippocampal CA3 pyramidal cells and to pyramidal cells in the visual cortex. In this model the input axons terminate on granule cells as well as on an inhibitory interneuron that projects to the granule cells. Stochastic secretion at these synapses involves both temporal variability in secretion at single synapses in the network as well as spatial variability in the secretion at different synapses. The role of this stochastic variability in controlling the size of the granule cell output to a level independent of the size of the input and in separating overlapping inputs has been determined analytically as well as by simulation. The regulation of granule-cell output activity to a reasonably constant value for different size inputs does not occur in the absence of an inhibitory interneuron when both spatial and temporal stochastic variability occurs at the remaining synapses; it is still very poor in the presence of such an interneuron but in the absence of stochastic variability. However, quite good regulation is achieved when the inhibitory interneuron is present with spatial and temporal stochastic variability of secretion at synapses in the network. Excellent regulation is achieved if, in addition, allowance is made for the nonlinear behaviour of the input-output characteristics of inhibitory interneurons. The capacity of granule-cell networks to separate overlapping patterns of activity on their inputs is adequate, with spatial variability in the secretion at synapses, but is improved if there is also temporal variability in the stochastic secretion at individual synapses, although this is at the expense of reliability in the network. Other factors which improve pattern separation are control of the output to very low activity levels, and a restriction on the cumulative size of the excitatory input terminals of each granule cell. Application of the theory to the input neural networks of the cerebellum and the hippocampus shows the role of stochastic variability in quantal transmission in determining the capacity of these networks for pattern separation and activity regulation.     

Associative recognition and storage in a model network of physiological neurons

We consider a neural network model in which the single neurons are chosen to closely resemble known physiological properties. The neurons are assumed to be linked by synapses which change their strength according to Hebbian rules on a short time scale (100ms). The dynamics of the network — the time evolution of the cell potentials and the synapses — is investigated by computer simulation. As in more abstract network models (Cooper 1973; Hopfield 1982; Kohonen 1984) it is found that the local dynamics of the cell potentials and the synaptic strengths result in global cooperative properties of the network and enable the network to process an incoming flux of information and to learn and store patterns associatively. A trained net can associate missing details of a pattern, can correct wrong details and can suppress noise in a pattern. The network can further abstract the prototype from a series of patterns with variations. A suitable coupling constant connecting the dynamics of the cell potentials with the synaptic strengths is derived by a mean field approximation. This coupling constant controls the neural sensitivity and thereby avoids both extremes of the network state, the state of permanent inactivity and the state of epileptic hyperactivity.     

T cell-dendritic cell immunological synapses contain TCR-dependent CD28-CD80 clusters that recruit protein kinase C theta

Short-lived TCR microclusters and a longer-lived protein kinase Ctheta-focusing central supramolecular activation cluster (cSMAC) have been defined in model immunological synapses (IS). In different model systems, CD28-mediated costimulatory interactions have been detected in microclusters, the cSMAC, or segregated from the TCR forming multiple distinct foci. The relationship between TCR and costimulatory molecules in the physiological IS of T cell-dendritic cell (DC) is obscure. To study the dynamic relationship of CD28-CD80 and TCR interactions in the T cell-DC IS during Ag-specific T cell activation, we generated CD80-eCFP mice using bacterial artificial chromosome transgenic technology. In splenic DCs, endogenous CD80 and CD80-eCFP localized to plasma membrane and Golgi apparatus, and CD80-eCFP was functional in vivo. In the OT-II T cell-DC IS, multiple segregated TCR, CD80, and LFA-1 clusters were detected. In the T cell-DC synapse CD80 clusters were colocalized with CD28 and PKCtheta, a characteristic of the cSMAC. Acute blockade of TCR signaling with anti-MHC Ab resulted in a rapid reduction in Ca(2+) signaling and the number and size of the CD80 clusters, a characteristic of TCR microclusters. Thus, the T cell-DC interface contains dynamic costimulatory foci that share characteristics of microclusters and cSMACs.     

Predicting metapopulation lifetime from macroscopic network properties

This paper presents a comparatively simple approximation formula for the mean life time of a metapopulation in a habitat network where habitat patch arrangement may be irregular and patch sizes differ. It is based on previous work on the development of an analytical approximation formula by Frank and Wissel [K. Frank, C. Wissel, A formula for the mean lifetime of metapopulations in heterogeneous landscapes, Am. Nat. 159 (2002) 530] and extends it by abstracting from individual patch locations. The mean metapopulation lifetime is expressed as a function of four macroscopic network properties: the ratio of dispersal range and network size, the ratio of range of environmental correlation and network size, and the total number and (geometric mean) size of the patches. The analysis takes into account that (ceteris paribus) patches close to the boundary of the habitat network contribute less to metapopulation survival than patches close to the centre of the network. Ignoring this fact can lead to a substantial overestimation of the mean metapopulation lifetime. Due to its numerical simplicity, the formula can be used as a conservation objective function even in complex network design problems where the number of patches to be allocated is very large. Numerical tests of the formula show that it performs very well within a wide range of network structures.     

High-speed high-resolution imaging of intercellular immune synapses using optical tweezers

Imaging in any plane other than horizontal in a microscope typically requires a reconstruction from multiple optical slices that significantly decreases the spatial and temporal resolution that can be achieved. This can limit the precision with which molecular events can be detected, for example, at intercellular contacts. This has been a major issue for the imaging of immune synapses between live cells, which has generally required the reconstruction of en face intercellular synapses, yielding spatial resolution significantly above the diffraction limit and updating at only a few frames per minute. Strategies to address this issue have usually involved using artificial activating substrates such as antibody-coated slides or supported planar lipid bilayers, but synapses with these surrogate stimuli may not wholly resemble immune synapses between two cells. Here, we combine optical tweezers and confocal microscopy to realize generally applicable, high-speed, high-resolution imaging of almost any arbitrary plane of interest. Applied to imaging immune synapses in live-cell conjugates, this has enabled the characterization of complex behavior of highly dynamic clusters of T cell receptors at the T cell/antigen-presenting cell intercellular immune synapse and revealed the presence of numerous, highly dynamic long receptor-rich filopodial structures within inhibitory Natural Killer cell immune synapses.     

On the size distribution of live genera

This article deals with the theoretical size (number of species) distribution of live genera, arising from a simple model of macroevolution in which speciations and extinctions are assumed to occur independently and at random, and in which new genera are formed by the random splitting of existing genera. Mathematically, the distribution is that of the state of a homogeneous birth-and-death process after an exponentially distributed time. An ordinary differential equation for the generating function of the distribution is derived and solved and a recurrence relation for computing the probabilities in the distribution presented. Some properties of the distribution, including asymptotic behaviour, are examined and the distribution of the time since establishment of a genus of a given size derived. Fitting the distribution to empirical taxon size distributions by maximum likelihood is discussed and two examples are presented.     

Topological cluster analysis reveals the systemic organization of the Caenorhabditis elegans connectome

The modular organization of networks of individual neurons interwoven through synapses has not been fully explored due to the incredible complexity of the connectivity architecture. Here we use the modularity-based community detection method for directed, weighted networks to examine hierarchically organized modules in the complete wiring diagram (connectome) of Caenorhabditis elegans (C. elegans) and to investigate their topological properties. Incorporating bilateral symmetry of the network as an important cue for proper cluster assignment, we identified anatomical clusters in the C. elegans connectome, including a body-spanning cluster, which correspond to experimentally identified functional circuits. Moreover, the hierarchical organization of the five clusters explains the systemic cooperation (e.g., mechanosensation, chemosensation, and navigation) that occurs among the structurally segregated biological circuits to produce higher-order complex behaviors.     

Network properties, species abundance and evolution in a model of evolutionary ecology

We study the evolution of the network properties of a populated network embedded in a genotype space characterized by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution produces two distinct types of network. When a specific genotype is only able to influence a few other genotypes, the ecosystem consists of separate non-interacting clusters (i.e. isolated compartments) in genotype space. When different types may influence a large number of other sites, the network becomes one large interconnected cluster. The distribution of interaction strengths--but not the number of connections--changes significantly with time. We find that the species abundance is only realistic for a high level of species connectivity. This suggests that real ecosystems form one interconnected whole in which selection leads to stronger interactions between the different types. Analogies with niche and neutral theory and assembly models are also considered.     

Neuronal, glial and synaptic remodeling in the adult hypothalamus: functional consequences and role of cell surface and extracellular matrix adhesion molecules

The adult hypothalamo-neurohypophysial system (HNS) undergoes activity-dependent morphological plasticity which modifies astrocytic coverage of its oxytocinergic neurons and their synaptic inputs. Thus, during physiological conditions that enhance central and peripheral release of oxytocin (OT), adjacent somata and dendrites of OT neurons become extensively juxtaposed, without intervening astrocytic processes and receive an increased number of synapses. The morphological changes occur within a few hours and are reversible with termination of stimulation. The reduced astrocytic coverage has direct functional consequences since it modifies extracellular ionic homeostasis, synaptic transmission, and the size and geometry of the extracellular space. It also contributes indirectly to neuronal function by permitting formation of synapses on neuronal surfaces freed of astrocytic processes. Overall, such remodeling is expected to potentiate activated neuronal firing, especially in clusters of tightly packed neurons, an anatomical arrangement characterizing OT neurons. This plasticity connotes dynamic cell interactions that must bring into play cell surface and extracellular matrix adhesive proteins like those intervening in developing neuronal systems undergoing neuronal-glial and synaptogenic transformations. It is worth noting, therefore, that adult HNS neurons and glia continue to express such molecules, including polysialic acid (PSA)-enriched neural cell adhesion molecule (PSA-NCAM) and the glycoprotein, tenascin-C. PSA is a large, complex sugar on the extracellular domain of NCAM considered a negative regulator of adhesion; it occurs in large amounts on the surfaces of HNS neurons and astrocytes. Tenascin-C, on the other hand, possesses adhesive and repulsive properties; it is secreted by HNS astrocytes and occurs in extracellular spaces and on cell surfaces after interaction with appropriate ligands. These molecules have been considered permissive factors for morphological plasticity. However, because of their localization and inherent properties, they may also serve to modulate the extracellular environment and in consequence, synaptic and volume transmission in a system in which the extracellular compartment is constantly being modified.