Spiking Activity Of Neurons Research Articles

Spike‐Based Spatiotemporal Processing Enabled by Oscillation Neuron for Energy‐Efficient Artificial Sensory Systems

Developing an energy‐efficient artificial sensory system is of great significance for neuroprosthesis, neurorobotics, and intelligent human–machine interfaces. Inspired by the biological perception, achieving this goal through spatiotemporal processing is viable. But some challenges, such as continuous signal coding resulting in high‐energy consumption, are yet to be solved, hindering the realization of human perception emulation. Herein, a perceptual simulation enabled by spike‐based spatiotemporal processing is demonstrated, which is analogous to the biological behavior, through an NbOx‐based oscillation neuron. The time difference between distinct inputs has a notable impact on the output spiking activity of oscillation neuron. On the basis of these features, the temporal‐related perceptions, for example, direction selectivity and sound localization are closely imitated. Unambiguous differentiation of direction or azimuth is enabled according to the output spiking numbers of oscillation neuron. Furthermore, by combining the oscillation neuron with a spiking neural network, azimuth recognition is conceptually established to mimic the human's response to auditory stimuli. Herein, the feasibility of employing spike‐based spatiotemporal processing of oscillation neurons to emulate sensory functionality, paving a highly potential way for realizing energy‐efficient artificial sensory systems, is proved.

Spontaneous Spiking Is Governed by Broadband Fluctuations.

Populations of cortical neurons generate rhythmic fluctuations in their ongoing spontaneous activity. These fluctuations can be seen in the local field potential (LFP), which reflects summed return currents from synaptic activity in the local population near a recording electrode. The LFP is spectrally broad, and many researchers view this breadth as containing many narrowband oscillatory components that may have distinct functional roles. This view is supported by the observation that the phase of narrowband oscillations is often correlated with cortical excitability and can relate to the timing of spiking activity and the fidelity of sensory evoked responses. Accordingly, researchers commonly tune in to these channels by narrowband filtering the LFP. Alternatively, neural activity may be fundamentally broadband and composed of transient, nonstationary rhythms that are difficult to approximate as oscillations. In this view, the instantaneous state of the broad ensemble relates directly to the excitability of the local population with no particular allegiance to any frequency band. To test between these alternatives, we asked whether the spiking activity of neocortical neurons in marmoset of either sex is better aligned with the phase of the LFP within narrow frequency bands or with a broadband measure. We find that the phase of broadband LFP fluctuations provides a better predictor of spike timing than the phase after filtering in narrow bands. These results challenge the view of the neocortex as a system composed of narrowband oscillators and supports a view in which neural activity fluctuations are intrinsically broadband.SIGNIFICANCE STATEMENT Research into the dynamical state of neural populations often attributes unique significance to the state of narrowband oscillatory components. However, rhythmic fluctuations in cortical activity are nonstationary and broad spectrum. We find that the timing of spontaneous spiking activity is better captured by the state of broadband fluctuations over any latent oscillatory component. These results suggest narrowband interpretations of rhythmic population activity may be limited, and broader representations may provide higher fidelity in describing moment-to-moment fluctuations in cortical activity.

Interlayer Connectivity Affects the Coherence Resonance and Population Activity Patterns in Two-Layered Networks of Excitatory and Inhibitory Neurons.

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

Tellurium‐Based Artificial Neuron: Capturing Biological Complexity While Keeping It Simple

AbstractNeuronal oscillation is critically involved in almost every cognitive task, including information coding, memory formation, and perception. This phenomenon is rooted in the spiking activity of neuron that is mediated by two principal ion‐channel mechanisms, i.e., fast Na+ mediated depolarization and delayed K+ mediated repolarization. In neuromorphic circuits, however, subcellular level of biocomplexity has routinely been traded off for smaller hardware overhead. Even so, the simplest artificial oscillatory neuron by far is still made of no less than two devices, a volatile memristor and a parallelly (serially) connected capacitor (resistor) that typically occupies relatively large circuit area. Herein, a simplest imaginable implementation is reported of the neuronal oscillation function in a single threshold switching device based on tellurium (Te). Thanks to the unique electrochemical‐thermal properties combined in Te, this device can exhibit self‐sustained oscillatory behavior when stimulated by a steady DC voltage as a result of the repetitive electrochemical growth and the ensuing Joule heat‐induced thermal melting of the Te filament, which phenomenologically capture the Na+ and K+ ion‐channel functions, respectively. This work broadens the neuromorphic applications of Te resistive switching devices from synaptic array devices to artificial neurons.

Brain Computer Interfaces: Wireless Recording of Brain Signals with Electro-Plasmonic Nanoantenna

Brain-computer interfaces (BCIs) recording brain signals via implantable sensors aims to substitute, restore, improve, add, or enhance human functions. However, wiring requirements for power transfer and signal transmission, acute immune response to implanted electrodes, and the limited scalability of the ever-popular microelectrode arrays prevent wide adaptation of BCIs. Here, we show that electro-plasmonic nanoparticles, plasmonic nanoparticles loaded with an electrochromic polymer, can overcome the limitations of the conventional implantable microelectrode arrays as BCI probes. Much like radio frequency identification (RFIDs) tags that use backscattering for remote readout, electro-plasmonic nanoparticles report the spiking activity of neurons by modulating the input light and the re-radiated light spectrum. Our electro-plasmonic nanoantennas are non-invasive, wire-free, highly sensitive (field sensitivity up to 15.5%) and require no surgical implantation. We believe that electro-plasmonic neural probes can help usher in a new era of BCIs.

Extrasynaptic NMDA Receptors Bidirectionally Modulate Intrinsic Excitability of Inhibitory Neurons.

The NMDA subtype glutamate receptors (NMDARs) play important roles in both physiological and pathologic processes in the brain. Compared with their critical roles in synaptic modifications and excitotoxicity in excitatory neurons, much less is understood about the functional contributions of NMDARs to the inhibitory GABAergic neurons. By using selective NMDAR inhibitors and potentiators, we here show that NMDARs bidirectionally modulate the intrinsic excitability (defined as spontaneous/evoked spiking activity and EPSP-spike coupling) in inhibitory GABAergic neurons in adult male and female mice. This modulation depends on GluN2C/2D- but not GluN2A/2B-containing NMDARs. We further show that NMDAR modulator EU1794-4 mostly enhances extrasynaptic NMDAR activity, and by using it we demonstrate a significant contribution of extrasynaptic NMDARs to the modulation of intrinsic excitability in inhibitory neurons. Together, this bidirectional modulation of intrinsic excitability reveals a previously less appreciated importance of NMDARs in the second-to-second functioning of inhibitory GABAergic neurons.SIGNIFICANCE STATEMENT NMDA subtype of glutamate receptors (NMDARs) have important roles in brain functions, including both physiological and pathologic ones. The role of NMDARs in inhibitory neurons has been less elucidated compared with that in excitatory neurons. Our results demonstrate the importance of GluN2C/GluN2D-containing but not GluN2A/GluN2B-containing extrasynaptic NMDARs in modulating the intrinsic excitability of inhibitory neurons. These results further suggest distinct contributions of subsynaptic locations and subunit compositions of NMDARs to their functions in excitatory and inhibitory neurons. The above findings have implications for better understanding of brain diseases, such as schizophrenia.

From mechanisms to functions: The role of theta and gamma coherence in the intrahippocampal circuits.

Brain rhythms are essential for information processing in neuronal networks. Oscillations recorded in different brain regions can be synchronized and have a constant phase difference, that is, they can be coherent. Coherence between local field potential (LFP) signals from different brain regions may be correlated with the performance of cognitive tasks, indicating that these regions of the brain are jointly involved in the information processing. Why does coherence occur and how is it related to the information transfer between different regions of the hippocampal formation? In this article, we discuss possible mechanisms of theta and gamma coherence and its role in the hippocampus-dependent attention and memory processes, since theta and gamma rhythms are most pronounced in these processes. We review in vivo studies of interactions between different regions of the hippocampal formation in theta and gamma frequency bands. The key propositions of the review are as follows: (1) coherence emerges from synchronous postsynaptic currents in principal neurons as a result of synchronization of neuronal spike activity; (2) the synchronization of neuronal spike patterns in two regions of the hippocampal formation can be realized through induction or resonance; (3) coherence at a specific time point reflects the transfer of information between the regions of the hippocampal formation; (4) the physiological roles of theta and gamma coherence are different due to their different functions and mechanisms of generation. All hippocampal neurons are involved in theta activity, and theta coherence arranges the firing order of principal neurons throughout the hippocampal formation. In contrast, gamma coherence reflects the coupling of active neuronal ensembles. Overall, the coherence of LFPs between different areas of the brain is an important physiological process based on the synchronized neuronal firing, and it is essential for cooperative information processing.

Propofol anesthesia concentration rather than abrupt behavioral unresponsiveness linearly degrades responses in the rat primary auditory cortex.

Despite extensive knowledge of its molecular and cellular effects, how anesthesia affects sensory processing remains poorly understood. In particular, it remains unclear whether anesthesia modestly or robustly degrades activity in primary sensory regions, and whether such changes are linked to anesthesia drug concentration versus behavioral unresponsiveness, which are typically confounded. Here, we used slow gradual intravenous propofol anesthesia induction together with auditory stimulation and intermittent assessment of behavioral responsiveness while recording epidural electroencephalogram, and neuronal spiking activity in primary auditory cortex (PAC) of eight rats. We found that all main components of neuronal activity including spontaneous firing rates, onset response magnitudes, onset response latencies, postonset neuronal silence duration, late-locking to 40Hz click-trains, and offset responses, gradually changed in a dose-dependent manner with increasing anesthesia levels without showing abrupt shifts around loss of righting reflex or other time-points. Thus, the dominant factor affecting PAC responses is the anesthesia drug concentration rather than any sudden, dichotomous behavioral state changes. Our findings explain a wide array of seemingly conflicting results in the literature that, depending on the precise definition of wakefulness (vigilant vs. drowsy) and anesthesia (light vs. deep/surgical), report a spectrum of effects in primary regions ranging from minimal to dramatic differences.

Kv3.1 channel expression determines the spike waveform in vocal-motor neurons

The speed and accuracy of fine motor skills depend on the spiking activity of upper motor neurons. In mammals, subclasses of these neurons contain unique excitable features that may enable the temporal precision required for these skills. Zebra finches are excellent models for testing how upper motor neurons provide the temporal precision required for rapid, precise behaviors. Their songs contain multiple, acoustically complex syllables, produced on sub-second time scales, and are controlled by pallial nuclei that form microcircuits analogous to those in the layered mammalian neocortex.

Effects of transcranial alternating current stimulation on spiking activity in computational models of single neocortical neurons

Neural oscillations are a key mechanism for information transfer in brain circuits. Rhythmic fluctuations of local field potentials control spike timing through cyclic membrane de- and hyperpolarization. Transcranial alternating current stimulation (tACS) is a non-invasive neuromodulation method which can directly interact with brain oscillatory activity by imposing an oscillating electric field on neurons. Despite its increasing use, the basic mechanisms of tACS are still not fully understood. Here, we investigate in a computational study the effects of tACS on morphologically realistic neurons with ongoing spiking activity. We characterize the membrane polarization as a function of electric field strength and subsequent effects on spiking activity in a set of 25 neurons from different neocortical layers. We find that tACS does not affect the firing rate of investigated neurons for electric field strengths applicable to human studies. However, we find that the applied electric fields entrain the spiking activity of large pyramidal neurons and large basket neurons at < 1 mV/mm field strengths. Our model results are in line with recent experimental studies and can provide a mechanistic framework to understand the effects of oscillating electric fields on single neuron activity. They highlight the importance of neuron morphology and biophysics in responsiveness to electrical stimulation.

TRPV1-Lineage Somatosensory Fibers Communicate with Taste Neurons in the Mouse Parabrachial Nucleus.

Trigeminal neurons convey somatosensory information from craniofacial tissues. In mouse brain, ascending projections from medullary trigeminal neurons arrive at taste neurons in the parabrachial (PB) nucleus, suggesting that taste neurons participate in somatosensory processing. However, the cell types that support this convergence were undefined. Using Cre-directed optogenetics and in vivo neurophysiology in anesthetized mice of both sexes, here we studied whether transient receptor potential vanilloid 1 (TRPV1)-lineage nociceptive and thermosensory fibers are primary neurons that drive trigeminal circuits reaching PB taste cells. We monitored spiking activity in individual PB neurons during photoexcitation of the terminals of TRPV1-lineage fibers arriving at the dorsal trigeminal nucleus caudalis, which relays orofacial somatosensory messages to the PB area. We also recorded PB neural responses to oral delivery of taste, chemesthetic, and thermal stimuli. We found that optical excitation of TRPV1-lineage fibers elicited responses in traditionally defined taste neurons in lateral PB nuclei. The tuning of neurons across diverse tastes associated with their sensitivity to TRPV1-lineage fiber stimulation, which only sparingly engaged neurons oriented to preferred tastes like sucrose. Moreover, neurons responsive to photostimulation of TRPV1-lineage afferents showed strong responses to temperature including noxious heat, which predominantly excited PB bitter taste cells. Multivariate and machine learning analyses revealed the PB confluence of TRPV1-lineage signals with taste captured sensory valence information shared across aversive gustatory, nociceptive, and thermal stimuli. Our results reveal that TRPV1-lineage fibers, which have defined roles in thermosensation and pain, communicate with PB taste neurons. This multisensory convergence supports dependencies between gustatory and somatosensory hedonic representations in the brain.SIGNIFICANCE STATEMENT The parabrachial (PB) nucleus participates in autonomic and integrative neural processing for diverse sensory modalities. We recently found in mice that trigeminal neurons supplying craniofacial somatosensation project to PB neurons sensitive to tastes. Here, we show that trigeminal projections to PB gustatory cells are driven by a genetic class of thermosensory and nociceptive fiber. Input from these fibers was associated with PB neural sensitivity to aversive oral temperatures and tastes and supported a multimodal neural representation of sensory valence across gustatory, nociceptive, and thermal stimuli. These results reveal gustation and somatosensation to be only components of a larger PB code that captures sensory value. Defining this circuit has implications for understanding the neural representation of taste, temperature, and also pain-related phenomena.

IDH-mutated gliomas promote epileptogenesis through d-2-hydroxyglutarate-dependent mTOR hyperactivation.

Uncontrolled seizures in patients with gliomas have a significant impact on quality of life and morbidity, yet the mechanisms through which these tumors cause seizures remain unknown. Here, we hypothesize that the active metabolite d-2-hydroxyglutarate (d-2-HG) produced by the IDH-mutant enzyme leads to metabolic disruptions in surrounding cortical neurons that consequently promote seizures. We use a complementary study of in vitro neuron-glial cultures and electrographically sorted human cortical tissue from patients with IDH-mutant gliomas to test this hypothesis. We utilize micro-electrode arrays for in vitro electrophysiological studies in combination with pharmacological manipulations and biochemical studies to better elucidate the impact of d-2-HG on cortical metabolism and neuronal spiking activity. We demonstrate that d-2-HG leads to increased neuronal spiking activity and promotes a distinct metabolic profile in surrounding neurons, evidenced by distinct metabolomic shifts and increased LDHA expression, as well as upregulation of mTOR signaling. The increases in neuronal activity are induced by mTOR activation and reversed with mTOR inhibition. Together, our data suggest that metabolic disruptions in the surrounding cortex due to d-2-HG may be a driving event for epileptogenesis in patients with IDH-mutant gliomas.

Distribution of spiking and bursting in Rulkov’s neuron model

Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.

Higuchi fractal dimension is a unique indicator of working memory content represented in spiking activity of visual neurons in extrastriate cortex.

Working memory has been identified as a top-down modulation of the average spiking activity in different brain parts. However, such modification has not yet been reported in the middle temporal (MT) cortex. A recent study showed that the dimensionality of the spiking activity of MT neurons increases after deployment of spatial working memory. This study is devoted to analyzing the ability of nonlinear and classical features to capture the content of the working memory from the spiking activity of MT neurons. The results suggest that only the Higuchi fractal dimension can be considered as a unique indicator of working memory while the Margaos-Sun fractal dimension, Shannon entropy, corrected conditional entropy, and skewness are perhaps indicators of other cognitive factors such as vigilance, awareness, and arousal as well as working memory.

Applying machine learning techniques to detect the deployment of spatial working memory from the spiking activity of MT neurons.

Neural signatures of working memory have been frequently identified in the spiking activity of different brain areas. However, some studies reported no memory-related change in the spiking activity of the middle temporal (MT) area in the visual cortex. However, recently it was shown that the content of working memory is reflected as an increase in the dimensionality of the average spiking activity of the MT neurons. This study aimed to find the features that can reveal memory-related changes with the help of machine-learning algorithms. In this regard, different linear and nonlinear features were obtained from the neuronal spiking activity during the presence and absence of working memory. To select the optimum features, the Genetic algorithm, Particle Swarm Optimization, and Ant Colony Optimization methods were employed. The classification was performed using the Support Vector Machine (SVM) and the K-Nearest Neighbor (KNN) classifiers. Our results suggest that the deployment of spatial working memory can be perfectly detected from spiking patterns of MT neurons with an accuracy of 99.65±0.12 using the KNN and 99.50±0.26 using the SVM classifiers.

Single neuron evidence of inattentional blindness in humans

Recording directly from the brain of a patient undergoing neurosurgery with electrodes implanted deep in her skull, we identified neurons that change their properties when the patient became consciously aware of content. Specifically, we showed the patient an established clip of a gorilla passing through the screen, unnoticeable, in a classic inattentional blindness task, and identified a neuron in the right amygdala that fired only when the patient was aware of the gorilla. A different neuron coded the moment of insight, when the patient realized that she had missed the salient gorilla in previous trials. A third cluster of neurons fired when the patient was exposed to a post-clip question (“How many passes did you count?“) and reflected on the content. Neurons in this cluster altered their response behavior between unaware and aware states.To investigate the interplay between the neurons' activity and characterize the potential cascade of information flow in the brain that leads to conscious awareness, we looked at the neurons' properties change, their activities’ alignment and the correlation across the cells. Examining the coherence between the spiking activity of the responsive neurons and the field potentials in neighboring sites we identified an alignment in the alpha and theta bands. This spike-field coherence hints at an involvement of attention and memory circuits in the perceptual awareness of the stimulus.Taken together, our results suggest that conscious awareness of content emerges when there is alignment between individual neurons' activity and the local field potentials. Our work provides direct neural correlate for the psychological process by which one can look at things directly but fail to perceive them with the “mind's eye”.

High-gamma mirror activity patterns in the human brain during reach-to-grasp movement observation, retention, and execution-An MEG study.

While the existence of a human mirror neuron system is evident, the involved brain areas and their exact functional roles remain under scientific debate. A number of functionally different mirror neuron types, neurons that selectively respond to specific grasp phases and types for example, have been reported with single cell recordings in monkeys. In humans, spatially limited, intracranially recorded electrophysiological signals in the high-gamma (HG) range have been used to investigate the human mirror system, as they are associated with spiking activity in single neurons. Our goal here is to complement previous intracranial HG studies by using magnetoencephalography to record HG activity simultaneously from the whole head. Participants performed a natural reach-to-grasp movement observation and delayed imitation task with different everyday objects and grasp types. This allowed us to characterize the spatial organization of cortical areas that show HG-activation modulation during movement observation (mirroring), retention (mnemonic mirroring), and execution (motor control). Our results show mirroring related HG modulation patterns over bilateral occipito-parietal as well as sensorimotor areas. In addition, we found mnemonic mirroring related HG modulation over contra-lateral fronto-temporal areas. These results provide a foundation for further human mirror system research as well as possible target areas for brain-computer interface and neurorehabilitation approaches.

Lactate is an energy substrate for rodent cortical neurons and enhances their firing activity.

Glucose is the mandatory fuel for the brain, yet the relative contribution of glucose and lactate for neuronal energy metabolism is unclear. We found that increased lactate, but not glucose concentration, enhances the spiking activity of neurons of the cerebral cortex. Enhanced spiking was dependent on ATP-sensitive potassium (KATP) channels formed with KCNJ11 and ABCC8 subunits, which we show are functionally expressed in most neocortical neuronal types. We also demonstrate the ability of cortical neurons to take-up and metabolize lactate. We further reveal that ATP is produced by cortical neurons largely via oxidative phosphorylation and only modestly by glycolysis. Our data demonstrate that in active neurons, lactate is preferred to glucose as an energy substrate, and that lactate metabolism shapes neuronal activity in the neocortex through KATP channels. Our results highlight the importance of metabolic crosstalk between neurons and astrocytes for brain function.

NCMP-07. IDH MUTANT GLIOMAS PROMOTE EPILEPTOGENESIS VIA D-2-HYDROXYGLUTARATE DEPENDENT MTOR HYPER-ACTIVATION

Abstract Uncontrolled seizures in patients with low grade gliomas have a significant impact on quality of life and morbidity, yet the mechanisms through which these tumors cause seizures remain unknown. Albeit there are multiple features that contribute to tumor related epileptogenesis, IDH mutations are determined to be an independent factor, although the pathogenesis remains poorly understood. Here, we hypothesize that the active metabolite D-2-hydroxyglutarate (D-2-HG) produced by the IDH-mutant enzyme leads to metabolic disruptions in surrounding cortical neurons that consequently promote seizures. We use a complementary study of in vitro cortical cultures and electrographically sorted human cortical tissue from patients (n=5) with IDH-mutant gliomas to test this hypothesis. We demonstrate that D-2-HG leads to increased neuronal spiking activity (p&amp;lt; 0.0001) and promotes a distinct metabolic profile in surrounding neurons and upregulation of mTOR signaling (p&amp;lt; 0.0001), which is consistent in human epileptic cortex compared to peritumoral nonepileptic cortex. Furthermore, increases in neuronal activity are induced by mTOR activation and reversed with mTOR inhibition. Together, our data suggest that metabolic disruptions and mTOR signaling upregulation in the surrounding cortex due to D-2-HG may be a driving event for epileptogenesis in patients with IDH-mutant low grade gliomas.

Spatial representability of neuronal activity

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.