Bump Attractor Research Articles

Network Models Predict That Pyramidal Neuron Hyperexcitability and Synapse Loss in the dlPFC Lead to Age-Related Spatial Working Memory Impairment in Rhesus Monkeys.

Behavioral studies have shown spatial working memory impairment with aging in several animal species, including humans. Persistent activity of layer 3 pyramidal dorsolateral prefrontal cortex (dlPFC) neurons during delay periods of working memory tasks is important for encoding memory of the stimulus. In vitro studies have shown that these neurons undergo significant age-related structural and functional changes, but the extent to which these changes affect neural mechanisms underlying spatial working memory is not understood fully. Here, we confirm previous studies showing impairment on the Delayed Recognition Span Task in the spatial condition (DRSTsp), and increased in vitro action potential firing rates (hyperexcitability), across the adult life span of the rhesus monkey. We use a bump attractor model to predict how empirically observed changes in the aging dlPFC affect performance on the Delayed Response Task (DRT), and introduce a model of memory retention in the DRSTsp. Persistent activity—and, in turn, cognitive performance—in both models was affected much more by hyperexcitability of pyramidal neurons than by a loss of synapses. Our DRT simulations predict that additional changes to the network, such as increased firing of inhibitory interneurons, are needed to account for lower firing rates during the DRT with aging reported in vivo. Synaptic facilitation was an essential feature of the DRSTsp model, but it did not compensate fully for the effects of the other age-related changes on DRT performance. Modeling pyramidal neuron hyperexcitability and synapse loss simultaneously led to a partial recovery of function in both tasks, with the simulated level of DRSTsp impairment similar to that observed in aging monkeys. This modeling work integrates empirical data across multiple scales, from synapse counts to cognitive testing, to further our understanding of aging in non-human primates.

Time-invariant working memory representations in the presence of code-morphing in the lateral prefrontal cortex

Maintenance of working memory is thought to involve the activity of prefrontal neuronal populations with strong recurrent connections. However, it was recently shown that distractors evoke a morphing of the prefrontal population code, even when memories are maintained throughout the delay. How can a morphing code maintain time-invariant memory information? We hypothesized that dynamic prefrontal activity contains time-invariant memory information within a subspace of neural activity. Using an optimization algorithm, we found a low-dimensional subspace that contains time-invariant memory information. This information was reduced in trials where the animals made errors in the task, and was also found in periods of the trial not used to find the subspace. A bump attractor model replicated these properties, and provided predictions that were confirmed in the neural data. Our results suggest that the high-dimensional responses of prefrontal cortex contain subspaces where different types of information can be simultaneously encoded with minimal interference.

Next-generation neural field model: The evolution of synchrony within patterns and waves.

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of θ-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.

Neural field model of memory-guided search.

Many organisms can remember locations they have previously visited during a search. Visual search experiments have shown exploration is guided away from these locations, reducing redundancies in the search path before finding a hidden target. We develop and analyze a two-layer neural field model that encodes positional information during a search task. A position-encoding layer sustains a bump attractor corresponding to the searching agent's current location, and search is modeled by velocity input that propagates the bump. A memory layer sustains persistent activity bounded by a wave front, whose edges expand in response to excitatory input from the position layer. Search can then be biased in response to remembered locations, influencing velocity inputs to the position layer. Asymptotic techniques are used to reduce the dynamics of our model to a low-dimensional system of equations that track the bump position and front boundary. Performance is compared for different target-finding tasks.

Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory

We analyze a multilayer neural field model of spatial working memory, focusing on the impact of interlaminar connectivity, spatial heterogeneity, and velocity inputs. Models of spatial working memory typically employ networks that generate persistent activity via a combination of local excitation and lateral inhibition. Our model comprises a multilayer set of equations that describes connectivity between neurons in the same and different layers using an integral term. The kernel of this integral term then captures the impact of different interlaminar connection strengths, spatial heterogeneity, and velocity input. We begin our analysis by focusing on how interlaminar connectivity shapes the form and stability of (persistent) bump attractor solutions to the model. Subsequently, we derive a low-dimensional approximation that describes how spatial heterogeneity, velocity input, and noise combine to determine the position of bump solutions. The main impact of spatial heterogeneity is to break the translation ...

Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction

We study the dynamics of stationary bumps in continuum neural field equations near a saddle-node bifurcation. The integral terms of these evolution equations have a weight kernel describing synaptic interactions between neurons at different locations of the network. Excited regions of the neural field correspond to parts of the domain whose fraction of active neurons exceeds a sharp threshold of a firing rate nonlinearity. For sufficiently low firing threshold, a stable bump coexists with an unstable bump and a homogeneous quiescent state. As the threshold is increased, the stable and unstable branch of bump solutions annihilate in a saddle-node bifurcation. Near this criticality, we derive a quadratic amplitude equation that describes the slow evolution of the even mode (bump contractions) as it depends on the distance from the bifurcation. Beyond the bifurcation, bumps eventually become extinct, and the lifetime of bumps increases for systems nearer the bifurcation. When noise is incorporated, a stochastic amplitude equation for the even mode can be derived, which can be analyzed to quantify bump extinction time both below and above the saddle-node.

Sensory feedback in a bump attractor model of path integration.

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.

A biophysical neural network model for visual working memory that accounts for memory binding errors

Binding errors, also called swap errors, occur in working memory tasks when the participant fails to report the feature of a previously presented target but the response is accurate relative to a non-target stimulus (for instance, s/he reports the of the green item when the red item's was to be reported). Psychophysical experiments have shown the importance of these errors in working memory tasks [1-3], and they reflect the failure of the system to maintain bundled through memory the conjunction of features that define one object. How the brain is able to integrate and maintain integrated several features of an item in one single memory is still an open question. Conjunctive selectivity, where single units are selective to combination of stimuli, has been suggested as a possible solution [4]. However, with the increase of features to encode the number of necessary neurons escalates exponentially. A hypothesis formulated for this problem in visual perception states that synchrony of different neural assemblies coding each of them a single feature of an item plays the main role [5]. This is an attractive hypothesis, because of its parsimonious and flexible neural representation: a particular neuron can participate in the coding of different objects at different times. Because under this hypothesis there is no hardwired selectivity for each group of features, it allows ex novo representations to emerge. Current neurophysiological data provides partial support for this idea but the specific neural mechanism remains unknown [5,6]. In order to understand this phenomenon and to test this synchrony hypothesis, we built a biophysical neural network model for the storage of items orks for working memory (ring models, as in [7]), one representing colors and the other one locations of equal eccentricity. These two networks are then connected via weak cortico-cortical excitation through AMPA synapses. With this model we are able to maintain persistent activity through recurrent synaptic interactions in memory [8] that encode colors and locations. AMPA synapses in recurrent excitation within each network induce gamma oscillations during bump activity through the interplay of fast excitation and slower feedback inhibition [7]. We found that when multiple are maintained within one ring model, the corresponding bump attractors oscillate out of synchrony with each other. In this model, the binding between and is effectively accomplished through the synchronization of gamma oscillations between individual in the two networks as a result of weak cortico-cortical excitation. As previously proposed [9-10], in our network model different memories are held at different phases of a low-frequency oscillation. In some simulations swap errors arise: color bumps abruptly change their phase and thus change their synchrony relationship with location bumps. This leads to a wrong association between and that may underlie memory binding errors reported in working memory tasks.

Cryptic laminar and columnar organization in the dorsolateral pallium of a weakly electric fish.

In the weakly electric gymnotiform fish, Apteronotus leptorhynchus, the dorsolateral pallium (DL) receives diencephalic inputs representing electrosensory input utilized for communication and navigation. Cell counts reveal that, similar to thalamocortical projections, many more cells are present in DL than in the diencephalic nucleus that provides it with sensory input. DL is implicated in learning and memory and considered homologous to medial and/or dorsal pallium. The gymnotiform DL has an apparently simple architecture with a random distribution of simple multipolar neurons. We used multiple neurotracer injections in order to study the microcircuitry of DL. Surprisingly, we demonstrated that the intrinsic connectivity of DL is highly organized. It consists of orthogonal laminar and vertical excitatory synaptic connections. The laminar synaptic connections are symmetric sparse, random, and drop off exponentially with distance; they parcellate DL into narrow (60 μm) overlapping cryptic layers. At distances greater than 100 μm, the laminar connections generate a strongly connected directed graph architecture within DL. The vertical connectivity suggests that DL is also organized into cryptic columns; these connections are highly asymmetric, with superficial DL cells preferentially projecting towards deeper cells. Our experimental analyses suggest that the overlapping cryptic columns have a width of 100 μm, in agreement with the minimal distance for strong connectivity. The architecture of DL and the expansive representation of its input, taken together with the strong expression of N-methyl-D-aspartate (NMDA) receptors by its cells, are consistent with theoretical ideas concerning the cortical computations of pattern separation and memory storage via bump attractors.

Subdiffusive dynamics of bump attractors: mechanisms and functional roles.

Bump attractors are localized activity patterns that can self-sustain after stimulus presentation, and they are regarded as the neural substrate for a host of perceptual and cognitive processes. One of the characteristic features of bump attractors is that they are neutrally stable, so that noisy inputs cause them to drift away from their initial locations, severely impairing the accuracy of bump location-dependent neural coding. Previous modeling studies of such noise-induced drifting activity of bump attractors have focused on normal diffusive dynamics, often with an assumption that noisy inputs are uncorrelated. Here we show that long-range temporal correlations and spatial correlations in neural inputs generated by multiple interacting bumps cause them to drift in an anomalous subdiffusive way. This mechanism for generating subdiffusive dynamics of bump attractors is further analyzed based on a generalized Langevin equation. We demonstrate that subdiffusive dynamics can significantly improve the coding accuracy of bump attractors, since the variance of the bump displacement increases sublinearly over time and is much smaller than that of normal diffusion. Furthermore, we reanalyze existing psychophysical data concerning the spread of recalled cue position in spatial working memory tasks and show that its variance increases sublinearly with time, consistent with subdiffusive dynamics of bump attractors. Based on the probability density function of bump position, we also show that the subdiffusive dynamics result in a long-tailed decay of firing rate, greatly extending the duration of persistent activity.

Correlated neuronal activity and its relationship to coding, dynamics and network architecture.

Correlated neuronal activity and its relationship to coding, dynamics and network architecture.

Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory

Prefrontal persistent activity during the delay of spatial working memory tasks is thought to maintain spatial location in memory. A 'bump attractor' computational model can account for this physiology and its relationship to behavior. However, direct experimental evidence linking parameters of prefrontal firing to the memory report in individual trials is lacking, and, to date, no demonstration exists that bump attractor dynamics underlies spatial working memory. We analyzed monkey data and found model-derived predictive relationships between the variability of prefrontal activity in the delay and the fine details of recalled spatial location, as evident in trial-to-trial imprecise oculomotor responses. Our results support a diffusing bump representation for spatial working memory instantiated in persistent prefrontal activity. These findings reinforce persistent activity as a basis for spatial working memory, provide evidence for a continuous prefrontal representation of memorized space and offer experimental support for bump attractor dynamics mediating cognitive tasks in the cortex.

Encoding certainty in bump attractors

Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit translational symmetry. Thus activity bumps are neutrally stable, and perturbations in position do not decay away. We extend previous work on bump attractors by constructing model networks capable of encoding the certainty or salience of a stimulus stored in memory. Such networks support bumps that are not only neutrally stable to perturbations in position, but also perturbations in amplitude. Possible bump solutions then lie on a two-dimensional attractor, determined by a continuum of positions and amplitudes. Such an attractor requires precisely balancing the strength of recurrent synaptic connections. The amplitude of activity bumps represents certainty, and is determined by the initial input to the system. Moreover, bumps with larger amplitudes are more robust to noise, and over time provide a more faithful representation of the stored stimulus. In networks with separate excitatory and inhibitory populations, generating bumps with a continuum of possible amplitudes, requires tuning the strength of inhibition to precisely cancel background excitation.

Impact of noise on theta-nested gamma oscillations in a spiking continuous attractor model of grid cells

Grid cells in the medial entorhinal cortex (MEC) encode location through firing fields that form grid-like maps of the environment. At the same time network activity in the MEC is dominated by oscillations in the theta (4-12 Hz) and gamma (30-100 Hz) bands. Our recent experimental data established that feedback inhibition between excitatory stellate cells and inhibitory fast spiking interneurons dominates the synaptic connectivity in layer II of the MEC, and that continuous attractor models derived from these properties are sufficient to explain both the network oscillations and grid firing fields [1]. Here we use a spiking continuous attractor network model of layer II stellate cells and fast spiking interneurons to examine the effect of intrinsic noise on the emergence of theta nested-gamma oscillations. In this model, stellate cells connect exclusively to interneurons, while interneurons contact only stellate cells. When driven with a theta (8 Hz) modulated external input, we observed network synchronization in the gamma range during the trough of the theta signal, which depended on the amount of intrinsic Gaussian noise generated independently at each neuron. Without noise, the network exhibited aberrant hyper-synchronous firing of a subpopulation of stellate cells at the beginning of each theta cycle. The stellate cell firing resulted in a strong feedback inhibitory postsynaptic currents from fast spiking interneurons that had an additional synchronizing effect. The strong inhibitory feedback abolished nested gamma oscillations. With increasing noise, the network entered an intermediate state in which we observed theta nested-gamma oscillations [1]. When noise level was set even higher, the nested gamma oscillations disappeared without increasing the amount of inhibitory coupling. We also present the impact of noise on bump attractor formation and gridness score of the grid-like receptive fields. Together, these results show that the presence of noise may have profound implications on the stability of theta-nested gamma oscillations in attractor neural circuits with feedback inhibition.

A spiking model of superior colliculus for bottom-up saliency

Active exploration of visual space is controlled by a saccadic system using a combination of bottom-up and top-down signals. Rate based models [1] and simple V1 models (e.g. [2]), have been proposed to explain bottom-up or attentional mechanisms. We present a biologically detailed spiking model of superior colliculus to generate saccadic eye movements using a competitive mechanism based on spike arrival times. Various pop-out tasks based on color, orientation features and motion is used to analyze the reaction time of the model. The superior colliculus is modeled as a two layer network with feature-specific superficial layers driving a common deep layer. The superficial layers of the superior colliculus are topologically organized and is driven by retinal parasols cells, V1 layer 2/3 orientation-selective cells, V1 layer 2/3 color-selective cells, and MT cells. These enable luminance, orientation, color and motion based popout respectively. In this model, the earliest spikes are considered the most salient. A saccade is triggered when there is a consistent winner in the superficial layers at the same spatial region over an extended period of time, 40 ms to 100 ms. The superficial layers implement a temporal winner-take-all mechanism; specifically, there exists a separate inhibitory subnetwork that allows each superficial layer to choose a winner. The deep layer integrates these winners over time and selects a single spatial region. It implements a bump attractor network mediated by short-range excitation (AMPA and NMDA) and long range inhibition, which generates a bump of activity before and during a saccade. An interesting property of bump attractor network based circuit is that a single cell response is independent of size of the stimulus. Similar spiking response was also observed in most of the visually selective superior colliculus cells in monkeys [3]. Additionally, this model captures known behavioral and neurophysiological properties of the superior colliculus such as saccadic suppression, activity buildup before saccade generation, and GABAb mediated inhibition from the deep layer to superficial layers resulting in selective inhibition in recently attended region. All the connections in the SC model are pre-wired to satisfy the response characteristics of superficial and deep layers. The reaction time of the model was tested on simple and conjunctive pop-out tasks. We observe only a mild shift in reaction time based on the number of distractors. Higher reaction time was observed as the complexity of the search task was increased. Also, reaction time increases based on the level of visual hierarchy that is connected to the superior colliculus layers.

Формирование самоорганизующихся отображений сенсорных сигналов на непрерывные нейросетевые аттракторы

In this article, we describe a simple binary neuron system, which implements a self-organized map. The system consists of R input neurons (R receptors), and N output neurons of a recurrent neural network. The neural network has a quasi-continuous set of attractor states (one-dimensional “bump attractor”). Due to the dynamics of the network, each external signal (i.e. activity state of receptors) imposes transition of the recurrent network into one of its stable states (points of its attractor). That makes our system different from the “winner takes all” construction of T.Kohonen. In case, when there is a one-dimensional cyclical manifold of external signals in R-dimensional input space, and the recurrent neural network presents a complete ring of neurons with local excitatory connections, there exists a process of learning of connections between the receptors and the neurons of the recurrent network, which enables a topologically correct mapping of input signals into the stable states of the neural network. The convergence rate of learning and the role of noises and other factors affecting the described phenomenon has been evaluated in computational simulations.

Interareal coupling reduces encoding variability in multi-area models of spatial working memory.

Persistent activity observed during delayed-response tasks for spatial working memory (Funahashi et al., 1989) has commonly been modeled by recurrent networks whose dynamics is described as a bump attractor (Compte et al., 2000). We examine the effects of interareal architecture on the dynamics of bump attractors in stochastic neural fields. Lateral inhibitory synaptic structure in each area sustains stationary bumps in the absence of noise. Introducing noise causes bumps in individual areas to wander as a Brownian walk. However, coupling multiple areas together can help reduce the variability of the bump's position in each area. To examine this quantitatively, we approximate the position of the bump in each area using a small noise expansion that also assumes weak amplitude interareal projections. Our asymptotic results show the motion of the bumps in each area can be approximated as a multivariate Ornstein–Uhlenbeck process. This shows reciprocal coupling between areas can always reduce variability, if sufficiently strong, even if one area contains much more noise than the other. However, when noise is correlated between areas, the variability-reducing effect of interareal coupling is diminished. Our results suggest that distributing spatial working memory representations across multiple, reciprocally-coupled brain areas can lead to noise cancelation that ultimately improves encoding.

From distributed resources to limited slots in multiple-item working memory: a spiking network model with normalization.

Recent behavioral studies have given rise to two contrasting models for limited working memory capacity: a "discrete-slot" model in which memory items are stored in a limited number of slots, and a "shared-resource" model in which the neural representation of items is distributed across a limited pool of resources. To elucidate the underlying neural processes, we investigated a continuous network model for working memory of an analog feature. Our model network fundamentally operates with a shared resource mechanism, and stimuli in cue arrays are encoded by a distributed neural population. On the other hand, the network dynamics and performance are also consistent with the discrete-slot model, because multiple objects are maintained by distinct localized population persistent activity patterns (bump attractors). We identified two phenomena of recurrent circuit dynamics that give rise to limited working memory capacity. As the working memory load increases, a localized persistent activity bump may either fade out (so the memory of the corresponding item is lost) or merge with another nearby bump (hence the resolution of mnemonic representation for the merged items becomes blurred). We identified specific dependences of these two phenomena on the strength and tuning of recurrent synaptic excitation, as well as network normalization: the overall population activity is invariant to set size and delay duration; therefore, a constant neural resource is shared by and dynamically allocated to the memorized items. We demonstrate that the model reproduces salient observations predicted by both discrete-slot and shared-resource models, and propose testable predictions of the merging phenomenon.

A model of propagating waves in cerebral cortex across network states

Propagating waves of activity have been measured in cerebral cortex in various experimental preparations, and show different propagation speed or patterns. Using network models, we investigated whether the “state” of the network can explain these differences. We used a modified version of a previous model, in which neuronal adaptation can facilitate the transition from activated, asynchronous irregular (AI) states to quiescence in random networks. [1] With a proper re-ignition mechanism, these networks can transition between UP/DOWN and AI states with different levels of adaptation. Here, we have studied the occurrence of propagating waves during this transition from UP/DOWN to self-sustained activated states in topographic spiking neural network models and compared these results to voltage-sensitive dye imaging data from the visual cortex, as well as to other known experimental results. The addition of local connections with realistic synaptic delays in these topographic spiking neural network models allows for the possibility of propagating slow waves in some network states. Further, while it is generally thought that the large, low-frequency propagation evoked by sensory stimulation during heavily anesthetized states gives way to a bump attractor during waking, activated states, we demonstrate the possibility that propagating activity exists throughout the whole spectrum of network activation and shifts from low frequency (predominantly controlled by adaptation) to high frequency (predominantly controlled by E/I interactions) as the level of network activation increases. With these results from network modeling, we aim to account both for observed effects of anesthesia on the spread of cortical activity in voltage-sensitive dye and electrophysiological experiments [2-4] and for the observation of traveling high-frequency oscillations in vitro [5] and in awake monkeys [6,7].

Similarity Effect and Optimal Control of Multiple-Choice Decision Making

Decision making with several choice options is central to cognition. To elucidate the neural mechanisms of such decisions, we investigated a recurrent cortical circuit model in which fluctuating spiking neural dynamics underlie trial-by-trial stochastic decisions. The model encodes a continuous analog stimulus feature and is thus applicable to multiple-choice decisions. Importantly, the continuous network captures similarity between alternatives and possible overlaps in their neural representation. Model simulations accounted for behavioral as well as single-unit neurophysiological data from a recent monkey experiment and revealed testable predictions about the patterns of error rate as a function of the similarity between the correct and actual choices. We also found that the similarity and number of options affect speed and accuracy of responses. A mechanism is proposed for flexible control of speed-accuracy tradeoff, based on a simple top-down signal to the decision circuit that may vary nonmonotonically with the number of choice alternatives.