Neural network model of the primary visual cortex: from functional architecture to lateral connectivity and back

Revisiting horizontal connectivity rules in V1: from like-to-like towards like-to-all

Horizontal connections in the primary visual cortex of carnivores, ungulates and primates organize on a near-regular lattice. Given the similar length scale for the regularity found in cortical orientation maps, the currently accepted theoretical standpoint is that these maps are underpinned by a like-to-like connectivity rule: horizontal axons connect preferentially to neurons with similar preferred orientation. However, there is reason to doubt the rule's explanatory power, since a growing number of quantitative studies show that the like-to-like connectivity preference and bias mostly observed at short-range scale, are highly variable on a neuron-to-neuron level and depend on the origin of the presynaptic neuron. Despite the wide availability of published data, the accepted model of visual processing has never been revised. Here, we review three lines of independent evidence supporting a much-needed revision of the like-to-like connectivity rule, ranging from anatomy to population functional measures, computational models and to theoretical approaches. We advocate an alternative, distance-dependent connectivity rule that is consistent with new structural and functional evidence: from like-to-like bias at short horizontal distance to like-to-all at long horizontal distance. This generic rule accounts for the observed high heterogeneity in interactions between the orientation and retinotopic domains, that we argue is necessary to process non-trivial stimuli in a task-dependent manner.

Global organization of neuronal activity only requires unstructured local connectivity

Modern electrophysiological recordings simultaneously capture single-unit spiking activities of hundreds of neurons spread across large cortical distances. Yet, this parallel activity is often confined to relatively low-dimensional manifolds. This implies strong coordination also among neurons that are most likely not even connected. Here, we combine in vivo recordings with network models and theory to characterize the nature of mesoscopic coordination patterns in macaque motor cortex and to expose their origin: We find that heterogeneity in local connectivity supports network states with complex long-range cooperation between neurons that arises from multi-synaptic, short-range connections. Our theory explains the experimentally observed spatial organization of covariances in resting state recordings as well as the behaviorally related modulation of covariance patterns during a reach-to-grasp task. The ubiquity of heterogeneity in local cortical circuits suggests that the brain uses the described mechanism to flexibly adapt neuronal coordination to momentary demands.

A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.

A hierarchy of theoretical approaches to study a neuronal network depends on a tradeoff between biological fidelity and mathematical tractibility. Biophysically-detailed models consider cellular mechanisms and anatomically defined synaptic circuits, but are often too complex to reveal insights into fundamental principles. In contrast, increasingly abstract reduced models facilitate analytical insights. To better ground the latter to the underlying biology, we describe a systematic procedure to move across the model hierarchy that allows understanding how changes in biological parameters—physiological, pathophysiological, or because of new data—impact the behaviour of the network. We apply this approach to mammalian primary visual cortex, and examine how the different models in the hierarchy reproduce functional signatures of this area, in particular the tuning of neurons to the orientation of a visual stimulus. Our work provides a navigation of the complex parameter space of neural network models faithful to biology, as well as highlighting how simplifications made for mathematical convenience can fundamentally change their behaviour.

Temporally coherent perturbation of neural dynamics during retention alters human multi-item working memory

Temporarily storing a list of items in working memory (WM), a fundamental ability in cognition, has been posited to rely on the temporal dynamics of multi-item neural representations during retention. However, the causal evidence, particularly in human subjects, is still lacking, let alone WM manipulation. Here, we develop a novel "dynamic perturbation" approach to manipulate the relative memory strength of WM items held in human brain, by presenting temporally correlated luminance sequences during retention to interfere with the multi-item neural dynamics. Six experiments on more than 150 subjects confirm the effectiveness of this WM manipulation approach. A computational model combining continuous attractor neural network (CANN) and short-term synaptic plasticity (STP) principles further reproduces all the empirical findings. The model reveals that the "dynamic perturbation" modifies the synaptic efficacies of WM items through STP principles, eventually leading to changes in their relative memory strengths. Our results support the causal role of temporal dynamics of neural network in mediating multi-item WM, and offer a promising, purely bottom-up approach to manipulate WM.

Propagation of BOLD Activity Reveals Task-dependent Directed Interactions Across Human Visual Cortex

It has recently been shown that large-scale propagation of blood-oxygen-level-dependent (BOLD) activity is constrained by anatomical connections and reflects transitions between behavioral states. It remains to be seen, however, if the propagation of BOLD activity can also relate to the brain's anatomical structure at a more local scale. Here, we hypothesized that BOLD propagation reflects structured neuronal activity across early visual field maps. To explore this hypothesis, we characterize the propagation of BOLD activity across V1, V2, and V3 using a modeling approach that aims to disentangle the contributions of local activity and directed interactions in shaping BOLD propagation. It does so by estimating the effective connectivity (EC) and the excitability of a noise-diffusion network to reproduce the spatiotemporal covariance structure of the data. We apply our approach to 7T fMRI recordings acquired during resting state (RS) and visual field mapping (VFM). Our results reveal different EC interactions and changes in cortical excitability in RS and VFM, and point to a reconfiguration of feedforward and feedback interactions across the visual system. We conclude that the propagation of BOLD activity has functional relevance, as it reveals directed interactions and changes in cortical excitability in a task-dependent manner.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

Interhemispheric Synchrony of Spontaneous Cortical States at the Cortical Column Level

In cat early visual cortex, neural activity patterns resembling evoked orientation maps emerge spontaneously under anesthesia. To test if such patterns are synchronized between hemispheres, we performed bilateral imaging in anesthetized cats using a new improved voltage-sensitive dye. We observed map-like activity patterns spanning early visual cortex in both hemispheres simultaneously. Patterns virtually identical to maps associated with the cardinal and oblique orientations emerged as leading principal components of the spontaneous fluctuations, and the strength of transient orientation states was correlated with their duration, providing evidence that these maps are transiently attracting states. A neural mass model we developed reproduced the dynamics of both smooth and abrupt orientation state transitions observed experimentally. The model suggests that map-like activity arises from slow modulations in spontaneous firing in conjunction with interplay between excitation and inhibition. Our results highlight the efficiency and functional precision of interhemispheric connectivity.

The Dynamical Regime of Sensory Cortex: Stable Dynamics around a Single Stimulus-Tuned Attractor Account for Patterns of Noise Variability

Correlated variability in cortical activity is ubiquitously quenched following stimulus onset, in a stimulus-dependent manner. These modulations have been attributed to circuit dynamics involving either multiple stable states (“attractors”) or chaotic activity. Here we show that a qualitatively different dynamical regime, involving fluctuations about a single, stimulus-driven attractor in a loosely balanced excitatory-inhibitory network (the stochastic “stabilized supralinear network”), best explains these modulations. Given the supralinear input/output functions of cortical neurons, increased stimulus drive strengthens effective network connectivity. This shifts the balance from interactions that amplify variability to suppressive inhibitory feedback, quenching correlated variability around more strongly driven steady states. Comparing to previously published and original data analyses, we show that this mechanism, unlike previous proposals, uniquely accounts for the spatial patterns and fast temporal dynamics of variability suppression. Specifying the cortical operating regime is key to understanding the computations underlying perception.

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A simple network model explains stimulus-tuning of cortical variability suppression

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Inhibition stabilizes recurrently interacting neurons with supralinear I/O functions

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Stimuli strengthen inhibitory stabilization around a stable state, quenching variability

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Single-trial V1 data are compatible with this model and rules out competing proposals

Toward a comprehensive understanding of the neural mechanisms of decoded neurofeedback

Real-time functional magnetic resonance imaging (fMRI) neurofeedback is an experimental framework in which fMRI signals are presented to participants in a real-time manner to change their behaviors. Changes in behaviors after real-time fMRI neurofeedback are postulated to be caused by neural plasticity driven by the induction of specific targeted activities at the neuronal level (targeted neural plasticity model). However, some research groups argued that behavioral changes in conventional real-time fMRI neurofeedback studies are explained by alternative accounts, including the placebo effect and physiological artifacts. Recently, decoded neurofeedback (DecNef) has been developed as a result of adapting new technological advancements, including implicit neurofeedback and fMRI multivariate analyses. DecNef provides strong evidence for the targeted neural plasticity model while refuting the abovementioned alternative accounts. In this review, we first discuss how DecNef refutes the alternative accounts. Second, we propose a model that shows how targeted neural plasticity occurs at the neuronal level during DecNef training. Finally, we discuss computational and empirical evidence that supports the model. Clarification of the neural mechanisms of DecNef would lead to the development of more advanced fMRI neurofeedback methods that may serve as powerful tools for both basic and clinical research.

Distributed network interactions and their emergence in developing neocortex

The principles governing the functional organization and development of long-range network interactions in the neocortex remain poorly understood. Using in vivo wide-field and 2-photon calcium imaging of spontaneous activity patterns in mature ferret visual cortex, we find widespread modular correlation patterns that accurately predict the local structure of visually-evoked orientation columns several millimeters away. Longitudinal imaging demonstrates that long-range spontaneous correlations are present early in cortical development prior to the elaboration of horizontal connections, and predict mature network structure. Silencing feed-forward drive through retinal or thalamic blockade does not eliminate early long-range correlated activity, suggesting a cortical origin. Circuit models containing only local, but heterogeneous, connections are sufficient to generate long-range correlated activity by confining activity patterns to a low-dimensional subspace via multi-synaptic short-range interactions. These results suggest that local connections in early cortical circuits can generate structured long-range network correlations that guide the formation of visually-evoked distributed functional networks.

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.

Neural field model to reconcile structure with function in primary visual cortex

Voltage-sensitive dye imaging experiments in primary visual cortex (V1) have shown that local, oriented visual stimuli elicit stable orientation-selective activation within the stimulus retinotopic footprint. The cortical activation dynamically extends far beyond the retinotopic footprint, but the peripheral spread stays non-selective-a surprising finding given a number of anatomo-functional studies showing the orientation specificity of long-range connections. Here we use a computational model to investigate this apparent discrepancy by studying the expected population response using known published anatomical constraints. The dynamics of input-driven localized states were simulated in a planar neural field model with multiple sub-populations encoding orientation. The realistic connectivity profile has parameters controlling the clustering of long-range connections and their orientation bias. We found substantial overlap between the anatomically relevant parameter range and a steep decay in orientation selective activation that is consistent with the imaging experiments. In this way our study reconciles the reported orientation bias of long-range connections with the functional expression of orientation selective neural activity. Our results demonstrate this sharp decay is contingent on three factors, that long-range connections are sufficiently diffuse, that the orientation bias of these connections is in an intermediate range (consistent with anatomy) and that excitation is sufficiently balanced by inhibition. Conversely, our modelling results predict that, for reduced inhibition strength, spurious orientation selective activation could be generated through long-range lateral connections. Furthermore, if the orientation bias of lateral connections is very strong, or if inhibition is particularly weak, the network operates close to an instability leading to unbounded cortical activation.

Phase-synchronization-based parcellation of resting state fMRI signals reveals topographically organized clusters in early visual cortex

Resting-state fMRI is widely used to study brain function and connectivity. However, interpreting patterns of resting state (RS) fMRI activity remains challenging as they may arise from different neuronal mechanisms than those triggered by exogenous events. Currently, this limits the use of RS-fMRI for understanding cortical function in health and disease. Here, we examine the phase synchronization (PS) properties of blood-oxygen level dependent (BOLD) signals obtained during visual field mapping (VFM) and RS with 7T fMRI. This data-driven approach exploits spatiotemporal covariations in the phase of BOLD recordings to establish the presence of clusters of synchronized activity. We find that, in both VFM and RS data, selecting the most synchronized neighboring recording sites identifies spatially localized PS clusters that follow the topographic organization of the visual cortex. However, in activity obtained during VFM, PS is spatially more extensive than in RS activity, likely reflecting stimulus-driven interactions between local responses. Nevertheless, the similarity of the PS clusters obtained for RS and stimulus-driven fMRI suggest that they share a common neuroanatomical origin. Our finding justifies and facilitates direct comparison of RS and stimulus-evoked activity.

Visual stimulation quenches global alpha range activity in awake primate V4: a case study

Increasing evidence suggests that sensory stimulation not only changes the level of cortical activity with respect to baseline but also its structure. Despite having been reported in a multitude of conditions and preparations (for instance, as a quenching of intertrial variability, Churchland et al., 2010), such changes remain relatively poorly characterized. Here, we used optical imaging of voltage-sensitive dyes to explore, in V4 of an awake macaque, the spatiotemporal characteristics of both visually evoked and spontaneously ongoing neuronal activity and their difference. With respect to the spontaneous case, we detected a reduction in large-scale activity ([Formula: see text]) in the alpha range (5 to 12.5 Hz) during sensory inflow accompanied by a decrease in pairwise correlations. Moreover, the spatial patterns of correlation obtained during the different visual stimuli were on the average more similar one to another than they were to that obtained in the absence of stimulation. Finally, these observed changes in activity dynamics approached saturation already at very low stimulus contrasts, unlike the progressive, near-linear increase of the mean raw evoked responses over a wide range of contrast values, which could indicate a specific switching in the presence of a sensory inflow.

The Influence of Mexican Hat Recurrent Connectivity on Noise Correlations and Stimulus Encoding

Noise correlations are a common feature of neural responses and have been observed in many cortical areas across different species. These correlations can influence information processing by enhancing or diminishing the quality of the neural code, but the origin of these correlations is still a matter of controversy. In this computational study we explore the hypothesis that noise correlations are the result of local recurrent excitatory and inhibitory connections. We simulated two-dimensional networks of adaptive spiking neurons with local connection patterns following Gaussian kernels. Noise correlations decay with distance between neurons but are only observed if the range of excitatory connections is smaller than the range of inhibitory connections (“Mexican hat” connectivity) and if the connection strengths are sufficiently strong. These correlations arise from a moving blob-like structure of evoked activity, which is absent if inhibitory interactions have a smaller range (“inverse Mexican hat” connectivity). Spatially structured external inputs fixate these blobs to certain locations and thus effectively reduce noise correlations. We further investigated the influence of these network configurations on stimulus encoding. On the one hand, the observed correlations diminish information about a stimulus encoded by a network. On the other hand, correlated activity allows for more precise encoding of stimulus information if the decoder has only access to a limited amount of neurons.

Itinerancy between attractor states in neural systems

Converging evidence from neural, perceptual and simulated data suggests that discrete attractor states form within neural circuits through learning and development. External stimuli may bias neural activity to one attractor state or cause activity to transition between several discrete states. Evidence for such transitions, whose timing can vary across trials, is best accrued through analyses that avoid any trial-averaging of data. One such method, hidden Markov modeling, has been effective in this context, revealing state transitions in many neural circuits during many tasks. Concurrently, modeling efforts have revealed computational benefits of stimulus processing via transitions between attractor states. This review describes the current state of the field, with comments on how its perceived limitations have been addressed.

Task-Driven Activity Reduces the Cortical Activity Space of the Brain: Experiment and Whole-Brain Modeling

How a stimulus or a task alters the spontaneous dynamics of the brain remains a fundamental open question in neuroscience. One of the most robust hallmarks of task/stimulus-driven brain dynamics is the decrease of variability with respect to the spontaneous level, an effect seen across multiple experimental conditions and in brain signals observed at different spatiotemporal scales. Recently, it was observed that the trial-to-trial variability and temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here we examined the dynamics of a large-scale model of the human cortex to provide a mechanistic understanding of these observations. The model allows computing the statistics of synaptic activity in the spontaneous condition and in putative tasks determined by external inputs to a given subset of brain regions. We demonstrated that external inputs decrease the variance, increase the covariances, and decrease the autocovariance of synaptic activity as a consequence of single node and large-scale network dynamics. Altogether, these changes in network statistics imply a reduction of entropy, meaning that the spontaneous synaptic activity outlines a larger multidimensional activity space than does the task-driven activity. We tested this model’s prediction on fMRI signals from healthy humans acquired during rest and task conditions and found a significant decrease of entropy in the stimulus-driven activity. Altogether, our study proposes a mechanism for increasing the information capacity of brain networks by enlarging the volume of possible activity configurations at rest and reliably settling into a confined stimulus-driven state to allow better transmission of stimulus-related information.

Task- or stimulus-related changes of brain dynamics have been the subject of intense investigation during the last years. One of the most robust hallmarks of task/stimulus-driven brain dynamics, as measured using diverse recording techniques, is the decrease of variability with respect to the spontaneous level. This has led several researchers to focus on the second-order statistics of evoked activity and to study their functional consequences for information processing. In particular, it was observed that the trial-to-trial variability (related to variable responses to an identical stimulus from one presentation to the next) and the temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here, we built a computational model of the whole brain to understand how local and large-scale brain dynamics contribute to these effects. The model allowed us to derive equations for the network statistics of both spontaneous and evoked activity. We observed that, as a consequence of single node and network dynamics, stimulus input impacts network statistics in such a way that the entropy of the stimulus-driven activity is lower than that during spontaneous activity. We confirmed this model prediction using empirical fMRI data and we further discuss its functional implications.

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.

Conductance-based refractory density model of primary visual cortex

A layered continual population model of primary visual cortex has been constructed, which reproduces a set of experimental data, including postsynaptic responses of single neurons on extracellular electric stimulation and spatially distributed activity patterns in response to visual stimulation. In the model, synaptically interacting excitatory and inhibitory neuronal populations are described by a conductance-based refractory density approach. Populations of two-compartment excitatory and inhibitory neurons in cortical layers 2/3 and 4 are distributed in the 2-d cortical space and connected by AMPA, NMDA and GABA type synapses. The external connections are pinwheel-like, according to the orientation of a stimulus. Intracortical connections are isotropic local and patchy between neurons with similar orientations. The model proposes better temporal resolution and more detailed elaboration than conventional mean-field models. In comparison to large network simulations, it excludes a posteriori statistical data manipulation and provides better computational efficiency and minimal parametrization.

Stimulus-dependent variability and noise correlations in cortical MT neurons

Population codes assume that neural systems represent sensory inputs through the firing rates of populations of differently tuned neurons. However, trial-by-trial variability and noise correlations are known to affect the information capacity of neural codes. Although recent studies have shown that stimulus presentation reduces both variability and rate correlations with respect to their spontaneous level, possibly improving the encoding accuracy, whether these second order statistics are tuned is unknown. If so, second-order statistics could themselves carry information, rather than being invariably detrimental. Here we show that rate variability and noise correlation vary systematically with stimulus direction in directionally selective middle temporal (MT) neurons, leading to characteristic tuning curves. We show that such tuning emerges in a stochastic recurrent network, for a set of connectivity parameters that overlaps with a single-state scenario and multistability. Information theoretic analysis shows that second-order statistics carry information that can improve the accuracy of the population code.

Associating spontaneous with evoked activity in a neural mass model of visual cortex

Spontaneous activity of the brain at rest frequently has been considered a mere backdrop to the salient activity evoked by external stimuli or tasks. However, the resting state of the brain consumes most of its energy budget, which suggests a far more important role. An intriguing hint comes from experimental observations of spontaneous activity patterns, which closely resemble those evoked by visual stimulation with oriented gratings, except that cortex appeared to cycle between different orientation maps. Moreover, patterns similar to those evoked by the behaviorally most relevant horizontal and vertical orientations occurred more often than those corresponding to oblique angles. We hypothesize that this kind of spontaneous activity develops at least to some degree autonomously, providing a dynamical reservoir of cortical states, which are then associated with visual stimuli through learning. To test this hypothesis, we use a biologically inspired neural mass model to simulate a patch of cat visual cortex. Spontaneous transitions between orientation states were induced by modest modifications of the neural connectivity, establishing a stable heteroclinic channel. Significantly, the experimentally observed greater frequency of states representing the behaviorally important horizontal and vertical orientations emerged spontaneously from these simulations. We then applied bar-shaped inputs to the model cortex and used Hebbian learning rules to modify the corresponding synaptic strengths. After unsupervised learning, different bar inputs reliably and exclusively evoked their associated orientation state; whereas in the absence of input, the model cortex resumed its spontaneous cycling. We conclude that the experimentally observed similarities between spontaneous and evoked activity in visual cortex can be explained as the outcome of a learning process that associates external stimuli with a preexisting reservoir of autonomous neural activity states. Our findings hence demonstrate how cortical connectivity can link the maintenance of spontaneous activity in the brain mechanistically to its core cognitive functions.

Neural network mechanisms underlying stimulus driven variability reduction

It is well established that the variability of the neural activity across trials, as measured by the Fano factor, is elevated. This fact poses limits on information encoding by the neural activity. However, a series of recent neurophysiological experiments have changed this traditional view. Single cell recordings across a variety of species, brain areas, brain states and stimulus conditions demonstrate a remarkable reduction of the neural variability when an external stimulation is applied and when attention is allocated towards a stimulus within a neuron's receptive field, suggesting an enhancement of information encoding. Using an heterogeneously connected neural network model whose dynamics exhibits multiple attractors, we demonstrate here how this variability reduction can arise from a network effect. In the spontaneous state, we show that the high degree of neural variability is mainly due to fluctuation-driven excursions from attractor to attractor. This occurs when, in the parameter space, the network working point is around the bifurcation allowing multistable attractors. The application of an external excitatory drive by stimulation or attention stabilizes one specific attractor, eliminating in this way the transitions between the different attractors and resulting in a net decrease in neural variability over trials. Importantly, non-responsive neurons also exhibit a reduction of variability. Finally, this reduced variability is found to arise from an increased regularity of the neural spike trains. In conclusion, these results suggest that the variability reduction under stimulation and attention is a property of neural circuits.

To understand how neurons encode information, neuroscientists record their firing activity while the animal executes a given task for many trials. Surprisingly, it has been found that the neural response is highly variable, which a priori limits the encoding of information by these neurons. However, recent experiments have shown that this variability is reduced when the animal receives a stimulus or attends to a particular one, suggesting an enhancement of information encoding. It is known that a cause of neural variability resides in the fact that individual neurons receive an input which fluctuates around their firing threshold. We demonstrate here that all the experimental results can naturally arise from the dynamics of a neural network. Using a realistic model, we show that the neural variability during spontaneous activity is particularly high because input noise induces large fluctuations between multiple –but unstable- network states. With stimulation or attention, one particular network state is stabilized and fluctuations decrease, leading to a neural variability reduction. In conclusion, our results suggest that the observed variability reduction is a property of the neural circuits of the brain.

Emergence of persistent networks in long-term intracranial EEG recordings

Over the past two decades, the increased ability to analyze network relationships among neural structures has provided novel insights into brain function. Most network approaches, however, focus on static representations of the brain's physical or statistical connectivity. Few studies have examined how brain functional networks evolve spontaneously over long epochs of continuous time. To address this, we examine functional connectivity networks deduced from continuous long-term electrocorticogram recordings. For a population of six human patients, we identify a persistent pattern of connections that form a frequency-band-dependent network template, and a set of core connections that appear frequently and together. These structures are robust, emerging from brief time intervals (~100 s) regardless of cognitive state. These results suggest that a metastable, frequency-band-dependent scaffold of brain connectivity exists from which transient activity emerges and recedes.

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119-138, 2006).

Short-Term Facilitation may Stabilize Parametric Working Memory Trace

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments. We propose that short-term synaptic facilitation in recurrent connections significantly improves the robustness of the model by slowing down the drift of activity bump. Extending the calculation of the drift velocity to network with synaptic facilitation, we conclude that facilitation can slow down the drift by a large factor, rendering the network suitable as a model of WM.

Statistical comparison of spike responses to natural stimuli in monkey area V1 with simulated responses of a detailed laminar network model for a patch of V1

A major goal of computational neuroscience is the creation of computer models for cortical areas whose response to sensory stimuli resembles that of cortical areas in vivo in important aspects. It is seldom considered whether the simulated spiking activity is realistic (in a statistical sense) in response to natural stimuli. Because certain statistical properties of spike responses were suggested to facilitate computations in the cortex, acquiring a realistic firing regimen in cortical network models might be a prerequisite for analyzing their computational functions. We present a characterization and comparison of the statistical response properties of the primary visual cortex (V1) in vivo and in silico in response to natural stimuli. We recorded from multiple electrodes in area V1 of 4 macaque monkeys and developed a large state-of-the-art network model for a 5 × 5-mm patch of V1 composed of 35,000 neurons and 3.9 million synapses that integrates previously published anatomical and physiological details. By quantitative comparison of the model response to the "statistical fingerprint" of responses in vivo, we find that our model for a patch of V1 responds to the same movie in a way which matches the statistical structure of the recorded data surprisingly well. The deviation between the firing regimen of the model and the in vivo data are on the same level as deviations among monkeys and sessions. This suggests that, despite strong simplifications and abstractions of cortical network models, they are nevertheless capable of generating realistic spiking activity. To reach a realistic firing state, it was not only necessary to include both N-methyl-d-aspartate and GABA(B) synaptic conductances in our model, but also to markedly increase the strength of excitatory synapses onto inhibitory neurons (>2-fold) in comparison to literature values, hinting at the importance to carefully adjust the effect of inhibition for achieving realistic dynamics in current network models.

A dynamic neural field model of mesoscopic cortical activity captured with voltage-sensitive dye imaging

A neural field model is presented that captures the essential non-linear characteristics of activity dynamics across several millimeters of visual cortex in response to local flashed and moving stimuli. We account for physiological data obtained by voltage-sensitive dye (VSD) imaging which reports mesoscopic population activity at high spatio-temporal resolution. Stimulation included a single flashed square, a single flashed bar, the line-motion paradigm--for which psychophysical studies showed that flashing a square briefly before a bar produces sensation of illusory motion within the bar--and moving squares controls. We consider a two-layer neural field (NF) model describing an excitatory and an inhibitory layer of neurons as a coupled system of non-linear integro-differential equations. Under the assumption that the aggregated activity of both layers is reflected by VSD imaging, our phenomenological model quantitatively accounts for the observed spatio-temporal activity patterns. Moreover, the model generalizes to novel similar stimuli as it matches activity evoked by moving squares of different speeds. Our results indicate that feedback from higher brain areas is not required to produce motion patterns in the case of the illusory line-motion paradigm. Physiological interpretation of the model suggests that a considerable fraction of the VSD signal may be due to inhibitory activity, supporting the notion that balanced intra-layer cortical interactions between inhibitory and excitatory populations play a major role in shaping dynamic stimulus representations in the early visual cortex.

Continuous attractors with morphed/correlated maps

Continuous attractor networks are used to model the storage and representation of analog quantities, such as position of a visual stimulus. The storage of multiple continuous attractors in the same network has previously been studied in the context of self-position coding. Several uncorrelated maps of environments are stored in the synaptic connections, and a position in a given environment is represented by a localized pattern of neural activity in the corresponding map, driven by a spatially tuned input. Here we analyze networks storing a pair of correlated maps, or a morph sequence between two uncorrelated maps. We find a novel state in which the network activity is simultaneously localized in both maps. In this state, a fixed cue presented to the network does not determine uniquely the location of the bump, i.e. the response is unreliable, with neurons not always responding when their preferred input is present. When the tuned input varies smoothly in time, the neuronal responses become reliable and selective for the environment: the subset of neurons responsive to a moving input in one map changes almost completely in the other map. This form of remapping is a non-trivial transformation between the tuned input to the network and the resulting tuning curves of the neurons. The new state of the network could be related to the formation of direction selectivity in one-dimensional environments and hippocampal remapping. The applicability of the model is not confined to self-position representations; we show an instance of the network solving a simple delayed discrimination task.

How is your position in an environment represented in the brain, and how does the representation distinguish between multiple environments? One of the proposed answers relies on continuous attractor neural networks. Consider the web page of your campus map as a network of pixels. Every pixel is a neuron, and nearby pixels excite each other, while distant pairs are inhibited. As a result of their interactions, a bunch of close-by pixels will light up, indicating your current position as suggested by your web-cam (the sensory input). When you travel to another campus, the common assumption holds that pixels are completely scrambled and the excitatory/inhibitory pattern of connections is summed to the existing one. Now these connections and the sensory input will activate the pixels corresponding to your location in the new campus. The active pixels will look like noise in the old map. But what if the campuses are similar, i.e. the pixels are not completely scrambled? We show that the network has a novel way of distinguishing between the environments, by lighting up distinct subsets of pixels for each campus. This emergent selectivity for the environment could be a mechanism underlying hippocampal remapping and directional selectivity of place cells in 1D environments.

Adaptive gain modulation in V1 explains contextual modifications during bisection learning

The neuronal processing of visual stimuli in primary visual cortex (V1) can be modified by perceptual training. Training in bisection discrimination, for instance, changes the contextual interactions in V1 elicited by parallel lines. Before training, two parallel lines inhibit their individual V1-responses. After bisection training, inhibition turns into non-symmetric excitation while performing the bisection task. Yet, the receptive field of the V1 neurons evaluated by a single line does not change during task performance. We present a model of recurrent processing in V1 where the neuronal gain can be modulated by a global attentional signal. Perceptual learning mainly consists in strengthening this attentional signal, leading to a more effective gain modulation. The model reproduces both the psychophysical results on bisection learning and the modified contextual interactions observed in V1 during task performance. It makes several predictions, for instance that imagery training should improve the performance, or that a slight stimulus wiggling can strongly affect the representation in V1 while performing the task. We conclude that strengthening a top-down induced gain increase can explain perceptual learning, and that this top-down signal can modify lateral interactions within V1, without significantly changing the classical receptive field of V1 neurons.

Spontaneous and driven cortical activity: implications for computation

The traditional view of spontaneous neural activity as 'noise' has been challenged by recent findings suggesting that: (a) spontaneous activity in cortical populations is highly structured in both space and time, (b) the spatio-temporal structure of spontaneous activity is linked to the underlying connectivity of the cortical network, (c) spontaneous cortical activity interacts with external stimulation to generate responses to the individual presentations of a stimulus, (d) network connectivity is shaped in part by the statistics of natural signals and (e) ongoing cortical activity represents a continuous top-down prediction/expectation signal that interacts with incoming input to generate an updated representation of the world. These results can be integrated to provide a new framework for the study of cortical computation.

Permitted and forbidden sets in discrete-time linear threshold recurrent neural networks

The concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks. Such concepts exhibit interesting dynamics in recurrent neural networks. This paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete-time recurrent neural networks. The linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks. Networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. The main contribution of this paper is to establish foundations of permitted and forbidden sets. Necessary and sufficient conditions for the linear threshold discrete-time recurrent neural networks are obtained for complete convergence, existence of permitted and forbidden sets, as well as conditionally multiattractivity, respectively. Simulation studies explore some possible interesting practical applications.

Topological analysis of population activity in visual cortex

Information in the cortex is thought to be represented by the joint activity of neurons. Here we describe how fundamental questions about neural representation can be cast in terms of the topological structure of population activity. A new method, based on the concept of persistent homology, is introduced and applied to the study of population activity in primary visual cortex (V1). We found that the topological structure of activity patterns when the cortex is spontaneously active is similar to those evoked by natural image stimulation and consistent with the topology of a two sphere. We discuss how this structure could emerge from the functional organization of orientation and spatial frequency maps and their mutual relationship. Our findings extend prior results on the relationship between spontaneous and evoked activity in V1 and illustrates how computational topology can help tackle elementary questions about the representation of information in the nervous system.

On the origin of the functional architecture of the cortex

The basic structure of receptive fields and functional maps in primary visual cortex is established without exposure to normal sensory experience and before the onset of the critical period. How the brain wires these circuits in the early stages of development remains unknown. Possible explanations include activity-dependent mechanisms driven by spontaneous activity in the retina and thalamus, and molecular guidance orchestrating thalamo-cortical connections on a fine spatial scale. Here I propose an alternative hypothesis: the blueprint for receptive fields, feature maps, and their inter-relationships may reside in the layout of the retinal ganglion cell mosaics along with a simple statistical connectivity scheme dictating the wiring between thalamus and cortex. The model is shown to account for a number of experimental findings, including the relationship between retinotopy, orientation maps, spatial frequency maps and cytochrome oxidase patches. The theory's simplicity, explanatory and predictive power makes it a serious candidate for the origin of the functional architecture of primary visual cortex.

Dynamics of Memory Representations in Networks with Novelty-Facilitated Synaptic Plasticity

The ability to associate some stimuli while differentiating between others is an essential characteristic of biological memory. Theoretical models identify memories as attractors of neural network activity, with learning based on Hebb-like synaptic modifications. Our analysis shows that when network inputs are correlated, this mechanism results in overassociations, even up to several memories "merging" into one. To counteract this tendency, we introduce a learning mechanism that involves novelty-facilitated modifications, accentuating synaptic changes proportionally to the difference between network input and stored memories. This mechanism introduces a dependency of synaptic modifications on previously acquired memories, enabling a wide spectrum of memory associations, ranging from absolute discrimination to complete merging. The model predicts that memory representations should be sensitive to learning order, consistent with recent psychophysical studies of face recognition and electrophysiological experiments on hippocampal place cells. The proposed mechanism is compatible with a recent biological model of novelty-facilitated learning in hippocampal circuitry.

Model-based analysis of excitatory lateral connections in the visual cortex

Excitatory lateral connections within the primary visual cortex are thought to link neurons with similar receptive field properties. Here we studied whether this rule can predict the distribution of excitatory connections in relation to cortical location and orientation preference in the cat visual cortex. To this end, we obtained orientation maps of areas 17 or 18 using optical imaging and injected anatomical tracers into these regions. The distribution of labeled axonal boutons originating from large populations of excitatory neurons was then analyzed and compared with that of individual pyramidal or spiny stellate cells. We demonstrate that the connection patterns of populations of nearby neurons can be reasonably predicted by Gaussian and von Mises distributions as a function of cortical location and orientation, respectively. The connections were best described by superposition of two components: a spatially extended, orientation-specific and a local, orientation-invariant component. We then fitted the same model to the connections of single cells. The composite pattern of nine excitatory neurons (obtained from seven different animals) was consistent with the assumptions of the model. However, model fits to single cell axonal connections were often poorer and their estimated spatial and orientation tuning functions were highly variable. We conclude that the intrinsic excitatory network is biased to similar cortical locations and orientations but it is composed of neurons showing significant deviations from the population connectivity rule.