Embedding of cortical representations by the superficial patch system

Markov Blankets and Mirror Symmetries-Free Energy Minimization and Mesocortical Anatomy

A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired patterns with mirror symmetry. Exchanges of synaptic flux in each pattern form coupled spatial eigenmodes, and the line of mirror reflection between the paired patterns operates as a Markov blanket, so that prediction errors in exchanges between the pairs are minimized. The theoretical analysis is then compared to the outcomes from a biological model of neocortical development, in which neuron precursors are selected by apoptosis for cell body and synaptic connections maximizing synchrony and also minimizing axonal length. It is shown that this model results in patterns of connection with the anticipated mirror symmetries, at micro-, meso- and inter-arial scales, among lateral connections, and in cortical depth. This explains the spatial organization and functional significance of neuron response preferences, and is compatible with the structural form of both columnar and noncolumnar cortex. Multi-way interactions of mirrored representations can provide a preliminary anatomically realistic model of cortical information processing.

Mutual consistency of multiple visual feature maps constrains combined map topology

The primary visual cortex (V1) is the first cortical area that processes visual information relayed from the thalamus. The topologies permitted in joint ocular dominance (OD), orientation preference (OP), and direction preference (DP) maps in V1 are considered, with the aim of finding a maximally symmetric periodic case that can serve as the basis for perturbations toward natural realizations. It is shown that mutual consistency of the maps selects just two possible such lattice structures, and that one of these is much closer to experiment than the other. This comprises a hexagonal lattice of alternating positive and negative OP singularities, with each unit cell or hypercolumn containing four such singularities, each of which radiates three DP discontinuities that follow OP contours and end at OP singularities of opposite sign. Other DP discontinuities emanate at 90 degrees to the midpoints of the ones that link OP singularities, and cross OP contours perpendicularly. These features explain experimentally observed relationships between DP discontinuities and OP contours, including sudden approximately 90-degree changes of direction in the former.

The large numbers of minicolumns in the primary visual cortex of humans, chimpanzees and gorillas are related to high visual acuity

Minicolumns are thought to be a fundamental neural unit in the neocortex and their replication may have formed the basis of the rapid cortical expansion that occurred during primate evolution. We sought evidence of minicolumns in the primary visual cortex (V-1) of three great apes, three rodents and representatives from three other mammalian orders: Eulipotyphla (European hedgehog), Artiodactyla (domestic pig) and Carnivora (ferret). Minicolumns, identified by the presence of a long bundle of radial, myelinated fibers stretching from layer III to the white matter of silver-stained sections, were found in the human, chimpanzee, gorilla and guinea pig V-1. Shorter bundles confined to one or two layers were found in the other species but represent modules rather than minicolumns. The inter-bundle distance, and hence density of minicolumns, varied systematically both within a local area that might represent a hypercolumn but also across the whole visual field. The distance between all bundles had a similar range for human, chimpanzee, gorilla, ferret and guinea pig: most bundles were 20-45 μm apart. By contrast, the space between bundles was greater for the hedgehog and pig (20-140 μm). The mean density of minicolumns was greater in tangential sections of the gorilla and chimpanzee (1,243-1,287 bundles/mm2) than in human (314-422 bundles/mm2) or guinea pig (643 bundles/mm2). The minicolumnar bundles did not form a hexagonal lattice but were arranged in thin curving and branched bands separated by thicker bands of neuropil/somata. Estimates of the total number of modules/minicolumns within V-1 were strongly correlated with visual acuity.

Traces of semantization - from episodic to semantic memory in a spiking cortical network model

Episodic memory is a recollection of past personal experiences associated with particular times and places. This kind of memory is commonly subject to loss of contextual information or" semantization", which gradually decouples the encoded memory items from their associated contexts while transforming them into semantic or gist-like representations. Novel extensions to the classical Remember/Know behavioral paradigm attribute the loss of episodicity to multiple exposures of an item in different contexts. Despite recent advancements explaining semantization at a behavioral level, the underlying neural mechanisms remain poorly understood. In this study, we suggest and evaluate a novel hypothesis proposing that Bayesian-Hebbian synaptic plasticity mechanisms might cause semantization of episodic memory. We implement a cortical spiking neural network model with a Bayesian-Hebbian learning rule called Bayesian Confidence Propagation Neural Network (BCPNN), which captures the semantization phenomenon and offers a mechanistic explanation for it. Encoding items across multiple contexts leads to item-context decoupling akin to semantization. We compare BCPNN plasticity with the more commonly used spike-timing dependent plasticity (STDP) learning rule in the same episodic memory task. Unlike BCPNN, STDP does not explain the decontextualization process. We further examine how selective plasticity modulation of isolated salient events may enhance preferential retention and resistance to semantization. Our model reproduces important features of episodicity on behavioral timescales under various biological constraints whilst also offering a novel neural and synaptic explanation for semantization, thereby casting new light on the interplay between episodic and semantic memory processes.Significance StatementRemembering single episodes is a fundamental attribute of cognition. Difficulties recollecting contextual information is a key sign of episodic memory loss or semantization. Behavioral studies demonstrate that semantization of episodic memory can occur rapidly, yet the neural mechanisms underlying this effect are insufficiently investigated. In line with recent behavioral findings, we show that multiple stimulus exposures in different contexts may advance item-context decoupling. We suggest a Bayesian-Hebbian synaptic plasticity hypothesis of memory semantization and further show that a transient modulation of plasticity during salient events may disrupt the decontextualization process by strengthening memory traces, and thus, enhancing preferential retention. The proposed cortical network-of-networks model thus bridges micro and mesoscale synaptic effects with network dynamics and behavior.

The growth of cognition: Free energy minimization and the embryogenesis of cortical computation

The assumption that during cortical embryogenesis neurons and synaptic connections are selected to form an ensemble maximising synchronous oscillation explains mesoscopic cortical development, and a mechanism for cortical information processing is implied by consistency with the Free Energy Principle and Dynamic Logic. A heteroclinic network emerges, with stable and unstable fixed points of oscillation corresponding to activity in symmetrically connected, versus asymmetrically connected, sets of neurons. Simulations of growth explain a wide range of anatomical observations for columnar and non-columnar cortex, superficial patch connections, and the organization and dynamic interactions of neurone response properties. An antenatal scaffold is created, upon which postnatal learning can establish continuously ordered neuronal representations, permitting matching of co-synchronous fields in multiple cortical areas to solve optimization problems as in Dynamic Logic. Fast synaptic competition partitions equilibria, minimizing "the curse of dimensionality", while perturbations between imperfectly partitioned synchronous fields, under internal reinforcement, enable the cortex to become adaptively self-directed. As learning progresses variational free energy is minimized and entropy bounded.

Gamma-band correlations in the primary visual cortex

This paper generalizes and extends previous work on using neural field theory to quantitatively analyze the two-dimensional (2D) spatiotemporal correlation properties of gamma-band (30-70 Hz) oscillations evoked by stimuli arriving at the primary visual cortex, and modulated by patchy connectivities that depend on orientation preference (OP). Correlation functions are derived analytically for general stimulus and measurement conditions. The theoretical results reproduce a range of published experimental results. These include (i) the existence of two-point oscillatory temporal cross correlations with zero time lag between neurons with similar OP; (ii) the influence of spatial separation of neurons on the strength of the correlations; and (iii) the effects of differing stimulus orientations. They go beyond prior work by incorporating experimentally observed patchy projection patterns to predict the 2D correlation structure including both OP and ocular dominance effects, thereby relaxing assumptions of translational invariance implicit in prior one-dimensional analysis.

A generative growth model for thalamocortical axonal branching in primary visual cortex

Axonal morphology displays large variability and complexity, yet the canonical regularities of the cortex suggest that such wiring is based on the repeated initiation of a small set of genetically encoded rules. Extracting underlying developmental principles can hence shed light on what genetically encoded instructions must be available during cortical development. Within a generative model, we investigate growth rules for axonal branching patterns in cat area 17, originating from the lateral geniculate nucleus of the thalamus. This target area of synaptic connections is characterized by extensive ramifications and a high bouton density, characteristics thought to preserve the spatial resolution of receptive fields and to enable connections for the ocular dominance columns. We compare individual and global statistics, such as a newly introduced length-weighted asymmetry index and the global segment-length distribution, of generated and biological branching patterns as the benchmark for growth rules. We show that the proposed model surpasses the statistical accuracy of the Galton-Watson model, which is the most commonly employed model for biological growth processes. In contrast to the Galton-Watson model, our model can recreate the log-normal segment-length distribution of the experimental dataset and is considerably more accurate in recreating individual axonal morphologies. To provide a biophysical interpretation for statistical quantifications of the axonal branching patterns, the generative model is ported into the physically accurate simulation framework of Cx3D. In this 3D simulation environment we demonstrate how the proposed growth process can be formulated as an interactive process between genetic growth rules and chemical cues in the local environment.

Introducing double bouquet cells into a modular cortical associative memory model

We present an electrophysiological model of double bouquet cells and integrate them into an established cortical columnar microcircuit model that has previously been used as a spiking attractor model for memory. Learning in that model relies on a Hebbian-Bayesian learning rule to condition recurrent connectivity between pyramidal cells. We here demonstrate that the inclusion of a biophysically plausible double bouquet cell model can solve earlier concerns about learning rules that simultaneously learn excitation and inhibition and might thus violate Dale’s principle. We show that learning ability and resulting effective connectivity between functional columns of previous network models is preserved when pyramidal synapses onto double bouquet cells are plastic under the same Hebbian-Bayesian learning rule. The proposed architecture draws on experimental evidence on double bouquet cells and effectively solves the problem of duplexed learning of inhibition and excitation by replacing recurrent inhibition between pyramidal cells in functional columns of different stimulus selectivity with a plastic disynaptic pathway. We thus show that the resulting change to the microcircuit architecture improves the model’s biological plausibility without otherwise impacting the model’s spiking activity, basic operation, and learning abilities.

A Scalable Multicore Architecture With Heterogeneous Memory Structures for Dynamic Neuromorphic Asynchronous Processors (DYNAPs)

Neuromorphic computing systems comprise networks of neurons that use asynchronous events for both computation and communication. This type of representation offers several advantages in terms of bandwidth and power consumption in neuromorphic electronic systems. However, managing the traffic of asynchronous events in large scale systems is a daunting task, both in terms of circuit complexity and memory requirements. Here, we present a novel routing methodology that employs both hierarchical and mesh routing strategies and combines heterogeneous memory structures for minimizing both memory requirements and latency, while maximizing programming flexibility to support a wide range of event-based neural network architectures, through parameter configuration. We validated the proposed scheme in a prototype multicore neuromorphic processor chip that employs hybrid analog/digital circuits for emulating synapse and neuron dynamics together with asynchronous digital circuits for managing the address-event traffic. We present a theoretical analysis of the proposed connectivity scheme, describe the methods and circuits used to implement such scheme, and characterize the prototype chip. Finally, we demonstrate the use of the neuromorphic processor with a convolutional neural network for the real-time classification of visual symbols being flashed to a dynamic vision sensor (DVS) at high speed.

Assessing the Role of Inhibition in Stabilizing Neocortical Networks Requires Large-Scale Perturbation of the Inhibitory Population

Neurons within cortical microcircuits are interconnected with recurrent excitatory synaptic connections that are thought to amplify signals (Douglas and Martin, 2007), form selective subnetworks (Ko et al., 2011), and aid feature discrimination. Strong inhibition (Haider et al., 2013) counterbalances excitation, enabling sensory features to be sharpened and represented by sparse codes (Willmore et al., 2011). This balance between excitation and inhibition makes it difficult to assess the strength, or gain, of recurrent excitatory connections within cortical networks, which is key to understanding their operational regime and the computations that they perform. Networks that combine an unstable high-gain excitatory population with stabilizing inhibitory feedback are known as inhibition-stabilized networks (ISNs) (Tsodyks et al., 1997). Theoretical studies using reduced network models predict that ISNs produce paradoxical responses to perturbation, but experimental perturbations failed to find evidence for ISNs in cortex (Atallah et al., 2012). Here, we reexamined this question by investigating how cortical network models consisting of many neurons behave after perturbations and found that results obtained from reduced network models fail to predict responses to perturbations in more realistic networks. Our models predict that a large proportion of the inhibitory network must be perturbed to reliably detect an ISN regime robustly in cortex. We propose that wide-field optogenetic suppression of inhibition under promoters targeting a large fraction of inhibitory neurons may provide a perturbation of sufficient strength to reveal the operating regime of cortex. Our results suggest that detailed computational models of optogenetic perturbations are necessary to interpret the results of experimental paradigms.SIGNIFICANCE STATEMENT Many useful computational mechanisms proposed for cortex require local excitatory recurrence to be very strong, such that local inhibitory feedback is necessary to avoid epileptiform runaway activity (an "inhibition-stabilized network" or "ISN" regime). However, recent experimental results suggest that this regime may not exist in cortex. We simulated activity perturbations in cortical networks of increasing realism and found that, to detect ISN-like properties in cortex, large proportions of the inhibitory population must be perturbed. Current experimental methods for inhibitory perturbation are unlikely to satisfy this requirement, implying that existing experimental observations are inconclusive about the computational regime of cortex. Our results suggest that new experimental designs targeting a majority of inhibitory neurons may be able to resolve this question.

Specific excitatory connectivity for feature integration in mouse primary visual cortex

Local excitatory connections in mouse primary visual cortex (V1) are stronger and more prevalent between neurons that share similar functional response features. However, the details of how functional rules for local connectivity shape neuronal responses in V1 remain unknown. We hypothesised that complex responses to visual stimuli may arise as a consequence of rules for selective excitatory connectivity within the local network in the superficial layers of mouse V1. In mouse V1 many neurons respond to overlapping grating stimuli (plaid stimuli) with highly selective and facilitatory responses, which are not simply predicted by responses to single gratings presented alone. This complexity is surprising, since excitatory neurons in V1 are considered to be mainly tuned to single preferred orientations. Here we examined the consequences for visual processing of two alternative connectivity schemes: in the first case, local connections are aligned with visual properties inherited from feedforward input (a 'like-to-like' scheme specifically connecting neurons that share similar preferred orientations); in the second case, local connections group neurons into excitatory subnetworks that combine and amplify multiple feedforward visual properties (a 'feature binding' scheme). By comparing predictions from large scale computational models with in vivo recordings of visual representations in mouse V1, we found that responses to plaid stimuli were best explained by assuming feature binding connectivity. Unlike under the like-to-like scheme, selective amplification within feature-binding excitatory subnetworks replicated experimentally observed facilitatory responses to plaid stimuli; explained selective plaid responses not predicted by grating selectivity; and was consistent with broad anatomical selectivity observed in mouse V1. Our results show that visual feature binding can occur through local recurrent mechanisms without requiring feedforward convergence, and that such a mechanism is consistent with visual responses and cortical anatomy in mouse V1.

Interlayer Repulsion of Retinal Ganglion Cell Mosaics Regulates Spatial Organization of Functional Maps in the Visual Cortex

In higher mammals, orientation tuning of neurons is organized into a quasi-periodic pattern in the primary visual cortex. Our previous model studies suggested that the topography of cortical orientation maps may originate from moiré interference of ON and OFF retinal ganglion cell (RGC) mosaics, but did not account for how the consistent spatial period of maps could be achieved. Here we address this issue with two crucial findings on the development of RGC mosaics: first, homotypic local repulsion between RGCs can develop a long-range hexagonal periodicity. Second, heterotypic interaction restrains the alignment of ON and OFF mosaics, and generates a periodic interference pattern map with consistent spatial frequency. To validate our model, we quantitatively analyzed the RGC mosaics in cat data, and confirmed that the observed retinal mosaics showed evidence of heterotypic interactions, contrary to the previous view that ON and OFF mosaics are developed independently.SIGNIFICANCE STATEMENT Orientation map is one of the most studied functional maps in the brain, but it has remained unanswered how the consistent spatial periodicity of maps could be developed. In the current study, we address this issue with our developmental model for the retinal origin of orientation map. We showed that local repulsive interactions between retinal ganglion cells (RGCs) can develop a hexagonal periodicity in the RGC mosaics and restrict the alignment between ON and OFF mosaics, so that they generate a periodic pattern with consistent spatial frequency for both the RGC mosaics and the cortical orientation maps. Our results demonstrate that the organization of functional maps in visual cortex, including its structural consistency, may be constrained by a retinal blueprint.

A Computational Analysis of the Function of Three Inhibitory Cell Types in Contextual Visual Processing

Most cortical inhibitory cell types exclusively express one of three genes, parvalbumin, somatostatin and 5HT3a. We conjecture that these three inhibitory neuron types possess distinct roles in visual contextual processing based on two observations. First, they have distinctive synaptic sources and targets over different spatial extents and from different areas. Second, the visual responses of cortical neurons are affected not only by local cues, but also by visual context. We use modeling to relate structural information to function in primary visual cortex (V1) of the mouse, and investigate their role in contextual visual processing. Our findings are three-fold. First, the inhibition mediated by parvalbumin positive (PV) cells mediates local processing and could underlie their role in boundary detection. Second, the inhibition mediated by somatostatin-positive (SST) cells facilitates longer range spatial competition among receptive fields. Third, non-specific top-down modulation to interneurons expressing vasoactive intestinal polypeptide (VIP), a subclass of 5HT3a neurons, can selectively enhance V1 responses.

A biological blueprint for the axons of superficial layer pyramidal cells in cat primary visual cortex

Pyramidal cells in the superficial layers of neocortex of higher mammals form a lateral network of axon clusters known as the 'daisy' network. The role of these axon clusters remains speculative and we still lack a comprehensive quantitative description of the single neurons forming the daisy or their heterogeneity. We filled intracellularly 50 superficial layer pyramidal neurons in the cat primary visual cortex and reconstructed the axonal tree and their synaptic boutons in 3D. Individual bouton clusters were identified using an objective mean-shift algorithm. By parameterizing the morphology of these 50 axonal trees and the 217 bouton clusters they formed, we were able to extract one set of relatively constant parameters and another set of variable parameters. Both sets combined allowed us to outline a comprehensive biological blueprint of superficial layer pyramidal neurons. Overall, our detailed analysis supports the hypothesis that pyramidal neurons use their lateral clusters to combine differential contextual cues, required for context-dependent processing of natural scenes.

Synaptic connections formed by patchy projections of pyramidal cells in the superficial layers of cat visual cortex

The present study is the first to describe quantitatively the patterns of synaptic connections made by the patchy network of pyramidal cell axons in the superficial layers of cat V1 in relation to the orientation map. Intrinsic signal imaging of the orientation map was combined with 3D morphological reconstructions of physiologically-characterized neurons at light and electron microscope levels. A Similarity Index (SI) expressed the similarity of the orientation domain of a given bouton cluster to that of its parent dendritic tree. Six pyramidal cells whose axons had a wide range of SIs were examined. Boutons were sampled from five local and five distal clusters, and from the linear segments that link the clusters. The synaptic targets were reconstructed by serial section electron microscopy. Of the 233 synapses examined, 182 synapses were formed with spiny neurons, the remainder with smooth neurons. The proportion of smooth neurons that were synaptic targets varied greatly (from 0 to 50%) between the cluster samples, but was not correlated with the SI. The postsynaptic density sizes were similar for synapses in local and distal clusters, regardless of their SI. This heterogeneity in the synaptic targets of single cells within the superficial layers is a network feature well-suited for context-dependent processing.

Further Work on the Shaping of Cortical Development and Function by Synchrony and Metabolic Competition

This paper furthers our attempts to resolve two major controversies-whether gamma synchrony plays a role in cognition, and whether cortical columns are functionally important. We have previously argued that the configuration of cortical cells that emerges in development is that which maximizes the magnitude of synchronous oscillation and minimizes metabolic cost. Here we analyze the separate effects in development of minimization of axonal lengths, and of early Hebbian learning and selective distribution of resources to growing synapses, by showing in simulations that these effects are partially antagonistic, but their interaction during development produces accurate anatomical and functional properties for both columnar and non-columnar cortex. The resulting embryonic anatomical order can provide a cortex-wide scaffold for postnatal learning that is dimensionally consistent with the representation of moving sensory objects, and, as learning progressively overwrites the embryonic order, further associations also occur in a dimensionally consistent framework. The role ascribed to cortical synchrony does not demand specific frequency, amplitude or phase variation of pulses to mediate "feature linking." Instead, the concerted interactions of pulse synchrony with short-term synaptic dynamics, and synaptic resource competition can further explain cortical information processing in analogy to Hopfield networks and quantum computation.

Axon topography of layer 6 spiny cells to orientation map in the primary visual cortex of the cat (area 18)

To uncover the functional topography of layer 6 neurons, optical imaging was combined with three-dimensional neuronal reconstruction. Apical dendrite morphology of 23 neurons revealed three distinct types. Type Aa possessed a short apical dendrite with many oblique branches, Type Ab was characterized by a short and less branched apical dendrite, whereas Type B had a long apical dendrite with tufts in layer 2. Each type had a similar number of boutons, yet their spatial distribution differed from each other in both radial and horizontal extent. Boutons of Type Aa and Ab were almost restricted to the column of the parent soma with a laminar preference to layer 4 and 5/6, respectively. Only Type B contributed to long horizontal connections (up to 1.5 mm) mostly in deep layers. For all types, bouton distribution on orientation map showed an almost equal occurrence at iso- (52.6 ± 18.8 %) and non-iso-orientation (oblique, 27.7 ± 14.9 % and cross-orientation 19.7 ± 10.9 %) sites. Spatial convergence of axons of nearby layer 6 spiny neurons depended on soma separation of the parent cells, but only weakly on orientation preference, contrary to orientation dependence of converging axons of layer 4 spiny cells. The results show that layer 6 connections have only a weak dependence on orientation preference compared with those of layers 2/3 (Buzás et al., J Comp Neurol 499:861–881, 2006) and 4 (Karube and Kisvárday, Cereb Cortex 21:1443–1458, 2011).

Voltage-Sensitive Dye Imaging of Neocortical Activity

Neural computations underlying sensory perception, cognition, and motor control are performed by populations of neurons at different anatomical and temporal scales. Few techniques are currently available for exploring the dynamics of local and large range populations. Voltage-sensitive dye imaging (VSDI), based on organic voltage probes, reveals neural population activity in areas ranging from a few tens of micrometers to a couple of centimeters, or two areas up to ~10 cm apart. VSDI provides a submillisecond temporal resolution and a spatial resolution of ~50 µm. The dye signal emphasizes subthreshold synaptic potentials. VSDI has been applied in the mouse, rat, gerbil, ferret, tree shrew, cat, and monkey cortices to explore the lateral spread of retinotopic or somatotopic activation; the dynamic spatiotemporal pattern resulting from sensory activation, including the somatosensory, olfactory, auditory, and visual modalities; and motor preparation and the properties of spontaneously occurring population activity. In this introduction, we focus on VSDI in vivo and review results obtained mostly in the visual system in our laboratory.

Modularity in the Organization of Mouse Primary Visual Cortex

Layer 1 (L1) of primary visual cortex (V1) is the target of projections from many brain regions outside of V1. We found that inputs to the non-columnar mouse V1 from the dorsal lateral geniculate nucleus and feedback projections from multiple higher cortical areas to L1 are patchy. The patches are matched to a pattern of M2 muscarinic acetylcholine receptor expression at fixed locations of mouse, rat, and monkey V1. Neurons in L2/3 aligned with M2-rich patches have high spatial acuity, whereas cells in M2-poor zones exhibited high temporal acuity. Together M2+ and M2- zones form constant-size domains that are repeated across V1. Domains map subregions of the receptive field, such that multiple copies are contained within the point image. The results suggest that the modular network in mouse V1 selects spatiotemporally distinct clusters of neurons within the point image for top-down control and differential routing of inputs to cortical streams.

Long-range recruitment of Martinotti cells causes surround suppression and promotes saliency in an attractor network model

Although the importance of long-range connections for cortical information processing has been acknowledged for a long time, most studies focused on the long-range interactions between excitatory cortical neurons. Inhibitory interneurons play an important role in cortical computation and have thus far been studied mainly with respect to their local synaptic interactions within the cortical microcircuitry. A recent study showed that long-range excitatory connections onto Martinotti cells (MC) mediate surround suppression. Here we have extended our previously reported attractor network of pyramidal cells (PC) and MC by introducing long-range connections targeting MC. We have demonstrated how the network with Martinotti cell-mediated long-range inhibition gives rise to surround suppression and also promotes saliency of locations at which simple non-uniformities in the stimulus field are introduced. Furthermore, our analysis suggests that the presynaptic dynamics of MC is only ancillary to its orientation tuning property in enabling the network with saliency detection. Lastly, we have also implemented a disinhibitory pathway mediated by another interneuron type (VIP interneurons), which inhibits MC and abolishes surround suppression.

Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks

The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection weighting modulated by physical proximity (i.e., asymmetric Euclidean random matrices), modular network partitioning, and functional specificity within the excitatory population. We present a set of analytical constraints that apply to the eigenvalue spectra of associated weight matrices, highlighting the relationship between connectivity rules and classes of network dynamics.

Möbius-strip-like columnar functional connections are revealed in somato-sensory receptive field centroids

Receptive fields of neurons in the forelimb region of areas 3b and 1 of primary somatosensory cortex, in cats and monkeys, were mapped using extracellular recordings obtained sequentially from nearly radial penetrations. Locations of the field centroids indicated the presence of a functional system in which cortical homotypic representations of the limb surfaces are entwined in three-dimensional Möbius-strip-like patterns of synaptic connections. Boundaries of somatosensory receptive field in nested groups irregularly overlie the centroid order, and are interpreted as arising from the superposition of learned connections upon the embryonic order. Since the theory of embryonic synaptic self-organization used to model these results was devised and earlier used to explain findings in primary visual cortex, the present findings suggest the theory may be of general application throughout cortex and may reveal a modular functional synaptic system, which, only in some parts of the cortex, and in some species, is manifest as anatomical ordering into columns.

Superficial layer pyramidal cells communicate heterogeneously between multiple functional domains of cat primary visual cortex

The axons of pyramidal neurons in the superficial layers of the neocortex of higher mammals form lateral networks of discrete clusters of synaptic boutons. In primary visual cortex the clusters are reported to link domains that share the same orientation preferences, but how individual neurons contribute to this network is unknown. Here we performed optical imaging to record the intrinsic signal, which is an indirect measure of neuronal firing, and determined the global map of orientation preferences in the cat primary visual system. In the same experiment, single cells were recorded and labelled intracellularly. We found that individual axons arborise within the retinotopic representation of the classical receptive field, but their bouton clusters were not aligned along their preferred axis of orientation along the retinotopic map. Axon clusters formed in a variety of different orientation domains, not just the like-orientation domains. This topography and heterogeneity of single-cell connectivity provides circuits for normalization and context-dependent feature processing of visual scenes.

Anatomical constraints on lateral competition in columnar cortical architectures

Competition is a well-studied and powerful mechanism for information processing in neuronal networks, providing noise rejection, signal restoration, decision making and associative memory properties, with relatively simple requirements for network architecture. Models based on competitive interactions have been used to describe the shaping of functional properties in visual cortex, as well as the development of functional maps in columnar cortex. These models require competition within a cortical area to occur on a wider spatial scale than cooperation, usually implemented by lateral inhibitory connections having a longer range than local excitatory connections. However, measurements of cortical anatomy reveal that the spatial extent of inhibition is in fact more restricted than that of excitation. Relatively few models reflect this, and it is unknown whether lateral competition can occur in cortical-like networks that have a realistic spatial relationship between excitation and inhibition. Here we analyze simple models for cortical columns and perform simulations of larger models to show how the spatial scales of excitation and inhibition can interact to produce competition through disynaptic inhibition. Our findings give strong support to the direct coupling effect-that the presence of competition across the cortical surface is predicted well by the anatomy of direct excitatory and inhibitory coupling and that multisynaptic network effects are negligible. This implies that for networks with short-range inhibition and longer-range excitation, the spatial extent of competition is even narrower than the range of inhibitory connections. Our results suggest the presence of network mechanisms that focus on intra-rather than intercolumn competition in neocortex, highlighting the need for both new models and direct experimental characterizations of lateral inhibition and competition in columnar cortex.

Developmental origin of patchy axonal connectivity in the neocortex: a computational model

Injections of neural tracers into many mammalian neocortical areas reveal a common patchy motif of clustered axonal projections. We studied in simulation a mathematical model for neuronal development in order to investigate how this patchy connectivity could arise in layer II/III of the neocortex. In our model, individual neurons of this layer expressed the activator-inhibitor components of a Gierer-Meinhardt reaction-diffusion system. The resultant steady-state reaction-diffusion pattern across the neuronal population was approximately hexagonal. Growth cones at the tips of extending axons used the various morphogens secreted by intrapatch neurons as guidance cues to direct their growth and invoke axonal arborization, so yielding a patchy distribution of arborization across the entire layer II/III. We found that adjustment of a single parameter yields the intriguing linear relationship between average patch diameter and interpatch spacing that has been observed experimentally over many cortical areas and species. We conclude that a simple Gierer-Meinhardt system expressed by the neurons of the developing neocortex is sufficient to explain the patterns of clustered connectivity observed experimentally.

Reactivation in working memory: an attractor network model of free recall

The dynamic nature of human working memory, the general-purpose system for processing continuous input, while keeping no longer externally available information active in the background, is well captured in immediate free recall of supraspan word-lists. Free recall tasks produce several benchmark memory phenomena, like the U-shaped serial position curve, reflecting enhanced memory for early and late list items. To account for empirical data, including primacy and recency as well as contiguity effects, we propose here a neurobiologically based neural network model that unifies short- and long-term forms of memory and challenges both the standard view of working memory as persistent activity and dual-store accounts of free recall. Rapidly expressed and volatile synaptic plasticity, modulated intrinsic excitability, and spike-frequency adaptation are suggested as key cellular mechanisms underlying working memory encoding, reactivation and recall. Recent findings on the synaptic and molecular mechanisms behind early LTP and on spiking activity during delayed-match-to-sample tasks support this view.

Reentry: a key mechanism for integration of brain function

Reentry in nervous systems is the ongoing bidirectional exchange of signals along reciprocal axonal fibers linking two or more brain areas. The hypothesis that reentrant signaling serves as a general mechanism to couple the functioning of multiple areas of the cerebral cortex and thalamus was first proposed in 1977 and 1978 (Edelman, 1978). A review of the amount and diversity of supporting experimental evidence accumulated since then suggests that reentry is among the most important integrative mechanisms in vertebrate brains (Edelman, 1993). Moreover, these data prompt testable hypotheses regarding mechanisms that favor the development and evolution of reentrant neural architectures.

Nested theta to gamma oscillations and precise spatiotemporal firing during memory retrieval in a simulated attractor network

Nested oscillations, where the phase of the underlying slow rhythm modulates the power of faster oscillations, have recently attracted considerable research attention as the increased phase-coupling of cross-frequency oscillations has been shown to relate to memory processes. Here we investigate the hypothesis that reactivations of memory patterns, induced by either external stimuli or internal dynamics, are manifested as distributed cell assemblies oscillating at gamma-like frequencies with life-times on a theta scale. For this purpose, we study the spatiotemporal oscillatory dynamics of a previously developed meso-scale attractor network model as a correlate of its memory function. The focus is on a hierarchical nested organization of neural oscillations in delta/theta (2-5Hz) and gamma frequency bands (25-35Hz), and in some conditions even in lower alpha band (8-12Hz), which emerge in the synthesized field potentials during attractor memory retrieval. We also examine spiking behavior of the network in close relation to oscillations. Despite highly irregular firing during memory retrieval and random connectivity within each cell assembly, we observe precise spatiotemporal firing patterns that repeat across memory activations at a rate higher than expected from random firing. In contrast to earlier studies aimed at modeling neural oscillations, our attractor memory network allows us to elaborate on the functional context of emerging rhythms and discuss their relevance. We provide support for the hypothesis that the dynamics of coherent delta/theta oscillations constitute an important aspect of the formation and replay of neuronal assemblies. This article is part of a Special Issue entitled Neural Coding 2012.

Effect of prestimulus alpha power, phase, and synchronization on stimulus detection rates in a biophysical attractor network model

Spontaneous oscillations measured by local field potentials, electroencephalograms and magnetoencephalograms exhibit a pronounced peak in the alpha band (8-12 Hz) in humans and primates. Both instantaneous power and phase of these ongoing oscillations have commonly been observed to correlate with psychophysical performance in stimulus detection tasks. We use a novel model-based approach to study the effect of prestimulus oscillations on detection rate. A previously developed biophysically detailed attractor network exhibits spontaneous oscillations in the alpha range before a stimulus is presented and transiently switches to gamma-like oscillations on successful detection. We demonstrate that both phase and power of the ongoing alpha oscillations modulate the probability of such state transitions. The power can either positively or negatively correlate with the detection rate, in agreement with experimental findings, depending on the underlying neural mechanism modulating the oscillatory power. Furthermore, the spatially distributed alpha oscillators of the network can be synchronized by global nonspecific weak excitatory signals. These synchronization events lead to transient increases in alpha-band power and render the network sensitive to the exact timing of target stimuli, making the alpha cycle function as a temporal mask in line with recent experimental observations. Our results are relevant to several studies that attribute a modulatory role to prestimulus alpha dynamics.

Stimulus detection rate and latency, firing rates and 1-40Hz oscillatory power are modulated by infra-slow fluctuations in a bistable attractor network model

Recordings of membrane and field potentials, firing rates, and oscillation amplitude dynamics show that neuronal activity levels in cortical and subcortical structures exhibit infra-slow fluctuations (ISFs) on time scales from seconds to hundreds of seconds. Similar ISFs are salient also in blood-oxygenation-level dependent (BOLD) signals as well as in psychophysical time series. Functional consequences of ISFs are not fully understood. Here, they were investigated along with dynamical implications of ISFs in large-scale simulations of cortical network activity. For this purpose, a biophysically detailed hierarchical attractor network model displaying bistability and operating in an oscillatory regime was used. ISFs were imposed as slow fluctuations in either the amplitude or frequency of fast synaptic noise. We found that both mechanisms produced an ISF component in the synthetic local field potentials (LFPs) and modulated the power of 1-40Hz oscillations. Crucially, in a simulated threshold-stimulus detection task (TSDT), these ISFs were strongly correlated with stimulus detection probabilities and latencies. The results thus show that several phenomena observed in many empirical studies emerge concurrently in the model dynamics, which yields mechanistic insight into how infra-slow excitability fluctuations in large-scale neuronal networks may modulate fast oscillations and perceptual processing. The model also makes several novel predictions that can be experimentally tested in future studies.

On the dynamics of cortical development: synchrony and synaptic self-organization

We describe a model for cortical development that resolves long-standing difficulties of earlier models. It is proposed that, during embryonic development, synchronous firing of neurons and their competition for limited metabolic resources leads to selection of an array of neurons with ultra-small-world characteristics. Consequently, in the visual cortex, macrocolumns linked by superficial patchy connections emerge in anatomically realistic patterns, with an ante-natal arrangement which projects signals from the surrounding cortex onto each macrocolumn in a form analogous to the projection of a Euclidean plane onto a Möbius strip. This configuration reproduces typical cortical response maps, and simulations of signal flow explain cortical responses to moving lines as functions of stimulus velocity, length, and orientation. With the introduction of direct visual inputs, under the operation of Hebbian learning, development of mature selective response “tuning” to stimuli of given orientation, spatial frequency, and temporal frequency would then take place, overwriting the earlier ante-natal configuration. The model is provisionally extended to hierarchical interactions of the visual cortex with higher centers, and a general principle for cortical processing of spatio-temporal images is sketched.

Link between orientation and retinotopic maps in primary visual cortex

Maps representing the preference of neurons for the location and orientation of a stimulus on the visual field are a hallmark of primary visual cortex. It is not yet known how these maps develop and what function they play in visual processing. One hypothesis postulates that orientation maps are initially seeded by the spatial interference of ON- and OFF-center retinal receptive field mosaics. Here we show that such a mechanism predicts a link between the layout of orientation preferences around singularities of different signs and the cardinal axes of the retinotopic map. Moreover, we confirm the predicted relationship holds in tree shrew primary visual cortex. These findings provide additional support for the notion that spatially structured input from the retina may provide a blueprint for the early development of cortical maps and receptive fields. More broadly, it raises the possibility that spatially structured input from the periphery may shape the organization of primary sensory cortex of other modalities as well.

Coverage, continuity, and visual cortical architecture

BACKGROUND

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far.

RESULTS

We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all the previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise.

CONCLUSIONS

Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.

Retinal origin of orientation maps in visual cortex

The orientation map is a hallmark of primary visual cortex in higher mammals. It is not yet known how orientation maps develop, what function they play in visual processing and why some species lack them. Here we advance the notion that quasi-periodic orientation maps are established by moiré interference of regularly spaced ON and OFF-center retinal ganglion cell mosaics. A key prediction of the theory is that the centers of iso-orientation domains must be arranged in a hexagonal lattice on the cortical surface. Here we show that such pattern is observed in individuals of four different species: monkey, cat, tree shrew and ferret. The proposed mechanism explains how orientation maps can develop without requiring precise patterns of spontaneous activity or molecular guidance. Further, it offers a possible account for the emergence of orientation tuning in single neurons despite the absence of orderly orientation maps in rodents species.