Grids from bands, or bands from grids? An examination of the effects of single unit contamination on grid cell firing fields

Exploiting semantic information in a spiking neural SLAM system

To navigate in new environments, an animal must be able to keep track of its position while simultaneously creating and updating an internal map of features in the environment, a problem formulated as simultaneous localization and mapping (SLAM) in the field of robotics. This requires integrating information from different domains, including self-motion cues, sensory, and semantic information. Several specialized neuron classes have been identified in the mammalian brain as being involved in solving SLAM. While biology has inspired a whole class of SLAM algorithms, the use of semantic information has not been explored in such work. We present a novel, biologically plausible SLAM model called SSP-SLAM-a spiking neural network designed using tools for large scale cognitive modeling. Our model uses a vector representation of continuous spatial maps, which can be encoded via spiking neural activity and bound with other features (continuous and discrete) to create compressed structures containing semantic information from multiple domains (e.g., spatial, temporal, visual, conceptual). We demonstrate that the dynamics of these representations can be implemented with a hybrid oscillatory-interference and continuous attractor network of head direction cells. The estimated self-position from this network is used to learn an associative memory between semantically encoded landmarks and their positions, i.e., an environment map, which is used for loop closure. Our experiments demonstrate that environment maps can be learned accurately and their use greatly improves self-position estimation. Furthermore, grid cells, place cells, and object vector cells are observed by this model. We also run our path integrator network on the NengoLoihi neuromorphic emulator to demonstrate feasibility for a full neuromorphic implementation for energy efficient SLAM.

Excitatory-inhibitory recurrent dynamics produce robust visual grids and stable attractors

Spatially modulated grid cells have been recently found in the rat secondary visual cortex (V2) during active navigation. However, the computational mechanism and functional significance of V2 grid cells remain unknown. To address the knowledge gap, we train a biologically inspired excitatory-inhibitory recurrent neural network to perform a two-dimensional spatial navigation task with multisensory input. We find grid-like responses in both excitatory and inhibitory RNN units, which are robust with respect to spatial cues, dimensionality of visual input, and activation function. Population responses reveal a low-dimensional, torus-like manifold and attractor. We find a link between functional grid clusters with similar receptive fields and structured excitatory-to-excitatory connections. Additionally, multistable torus-like attractors emerged with increasing sparsity in inter- and intra-subnetwork connectivity. Finally, irregular grid patterns are found in recurrent neural network (RNN) units during a visual sequence recognition task. Together, our results suggest common computational mechanisms of V2 grid cells for spatial and non-spatial tasks.

Spike Sorting of Non-Stationary Data in Successive Intervals Based on Dirichlet Process Mixtures

This paper proposes a new automatic method for spike sorting and tracking non-stationary data based on the Dirichlet Process Mixture (DPM). Data is divided into non-overlapping intervals and mixtures are applied to individual frames rather than to the whole data. In this paper, we have used the information of the previous frame to estimate the cluster parameters of the current interval. Specifically, the means of the clusters in the previous frame are used for estimating the cluster means of the current one, and other parameters are estimated via noninformative priors. The proposed method is capable to track variations in size, shape, or location of clusters as well as detecting the appearance and disappearance of them. We present results in two-dimensional space of first and second principal components (PC1-PC2), but any other feature extraction method leading to the ability of modeling spikes with Normal or t-Student distributions can also be applied. Application of this approach to simulated data and the recordings from anesthetized rat hippocampus confirms its superior performance in comparison to a standard DPM that uses no information from previous frames.

From End to End: Gaining, Sorting, and Employing High-Density Neural Single Unit Recordings

The meaning behind neural single unit activity has constantly been a challenge, so it will persist in the foreseeable future. As one of the most sourced strategies, detecting neural activity in high-resolution neural sensor recordings and then attributing them to their corresponding source neurons correctly, namely the process of spike sorting, has been prevailing so far. Support from ever-improving recording techniques and sophisticated algorithms for extracting worthwhile information and abundance in clustering procedures turned spike sorting into an indispensable tool in electrophysiological analysis. This review attempts to illustrate that in all stages of spike sorting algorithms, the past 5 years innovations' brought about concepts, results, and questions worth sharing with even the non-expert user community. By thoroughly inspecting latest innovations in the field of neural sensors, recording procedures, and various spike sorting strategies, a skeletonization of relevant knowledge lays here, with an initiative to get one step closer to the original objective: deciphering and building in the sense of neural transcript.

Cortical processing of flexible and context-dependent sensorimotor sequences

The brain generates complex sequences of movements that can be flexibly configured based on behavioural context or real-time sensory feedback1, but how this occurs is not fully understood. Here we developed a 'sequence licking' task in which mice directed their tongue to a target that moved through a series of locations. Mice could rapidly branch the sequence online based on tactile feedback. Closed-loop optogenetics and electrophysiology revealed that the tongue and jaw regions of the primary somatosensory (S1TJ) and motor (M1TJ) cortices2 encoded and controlled tongue kinematics at the level of individual licks. By contrast, the tongue 'premotor' (anterolateral motor) cortex3-10 encoded latent variables including intended lick angle, sequence identity and progress towards the reward that marked successful sequence execution. Movement-nonspecific sequence branching signals occurred in the anterolateral motor cortex and M1TJ. Our results reveal a set of key cortical areas for flexible and context-informed sequence generation.

A geometric attractor mechanism for self-organization of entorhinal grid modules

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

Hippocampal Sequences During Exploration: Mechanisms and Functions

Although the hippocampus plays a critical role in spatial and episodic memories, the mechanisms underlying memory formation, stabilization, and recall for adaptive behavior remain relatively unknown. During exploration, within single cycles of the ongoing theta rhythm that dominates hippocampal local field potentials, place cells form precisely ordered sequences of activity. These neural sequences result from the integration of both external inputs conveying sensory-motor information, and intrinsic network dynamics possibly related to memory processes. Their endogenous replay during subsequent sleep is critical for memory consolidation. The present review discusses possible mechanisms and functions of hippocampal theta sequences during exploration. We present several lines of evidence suggesting that these neural sequences play a key role in information processing and support the formation of initial memory traces, and discuss potential functional distinctions between neural sequences emerging during theta vs. awake sharp-wave ripples.

A local measure of symmetry and orientation for individual spikes of grid cells

Grid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.

Functional properties of stellate cells in medial entorhinal cortex layer II

Layer II of the medial entorhinal cortex (MEC) contains two principal cell types: pyramidal cells and stellate cells. Accumulating evidence suggests that these two cell types have distinct molecular profiles, physiological properties, and connectivity. The observations hint at a fundamental functional difference between the two cell populations but conclusions have been mixed. Here, we used a tTA-based transgenic mouse line to drive expression of ArchT, an optogenetic silencer, specifically in stellate cells. We were able to optogenetically identify stellate cells and characterize their firing properties in freely moving mice. The stellate cell population included cells from a range of functional cell classes. Roughly one in four of the tagged cells were grid cells, suggesting that stellate cells contribute not only to path-integration-based representation of self-location but also have other functions. The data support observations suggesting that grid cells are not the sole determinant of place cell firing.

Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity

Neurons in the hippocampus and adjacent brain areas show a large diversity in their tuning to location and head direction, and the underlying circuit mechanisms are not yet resolved. In particular, it is unclear why certain cell types are selective to one spatial variable, but invariant to another. For example, place cells are typically invariant to head direction. We propose that all observed spatial tuning patterns - in both their selectivity and their invariance - arise from the same mechanism: Excitatory and inhibitory synaptic plasticity driven by the spatial tuning statistics of synaptic inputs. Using simulations and a mathematical analysis, we show that combined excitatory and inhibitory plasticity can lead to localized, grid-like or invariant activity. Combinations of different input statistics along different spatial dimensions reproduce all major spatial tuning patterns observed in rodents. Our proposed model is robust to changes in parameters, develops patterns on behavioral timescales and makes distinctive experimental predictions.

Comparison of combined spike detection and clustering using mutual information

BACKGROUND

Spike sorting techniques involve both detection of spike waveform events and classification of those events into clusters of similar waveform shape. The one existing method of evaluating the combined effects of both detection and classification depends on assignment of cluster correspondence. Other methods of evaluation have focused on either clustering or detection, but not both, although these two steps may interact.

NEW METHOD

This paper develops an information theoretic measure of agreement between the output of two spike sorting techniques, AMI_all, which can be used even when the number of waveform events detected by the two techniques differs.

RESULTS

AMI_all is shown to be a useful measure for studying variations of parameters of spike sorting techniques in two examples: comparing outputs for simulated noisy spike sorting and spike sorting of human single neuron recordings. Comparison with existing methods Computing AMI_all does not require an explicit assignment of cluster correspondence, thereby eliminating a potential source of variation. By providing a single measure of performance, computing AMI_all is very useful when comparing large numbers of algorithmic or parametric variations of spike sorting techniques; prior comparison techniques have often required multiple measures of performance which complicates large scale comparisons.

CONCLUSIONS

The use of AMI_all to measure agreement between spike sorting techniques facilitates the comparison of the outputs of those techniques, including variations in both spike detection and waveform clustering. This measure should be useful for broad based and large scale comparisons between spike sorting techniques.

Theta sequences of grid cell populations can provide a movement-direction signal

It has been proposed that path integration in mammals is performed by the convergence of internally generated speed and directional inputs onto grid cells. Although this hypothesis has been supported by the discovery that head direction, speed, and grid cells are intermixed within entorhinal cortex and by the recent finding that head-direction inputs are necessary for grid firing, many details on how grid cells are generated have remained elusive. For example, analysis of recording data suggests that substituting head direction for movement direction accrues errors that preclude the formation of grid patterns. To address this discrepancy, we propose that the organization of grid networks makes it plausible that movement-direction signals are an output from grid cells and that temporally precise grid cell sequences provide a robust directional signal to other spatial and directional cell types.

Context-dependent spatially periodic activity in the human entorhinal cortex

The spatially periodic activity of grid cells in the entorhinal cortex (EC) of the rodent, primate, and human provides a coordinate system that, together with the hippocampus, informs an individual of its location relative to the environment and encodes the memory of that location. Among the most defining features of grid-cell activity are the 60° rotational symmetry of grids and preservation of grid scale across environments. Grid cells, however, do display a limited degree of adaptation to environments. It remains unclear if this level of environment invariance generalizes to human grid-cell analogs, where the relative contribution of visual input to the multimodal sensory input of the EC is significantly larger than in rodents. Patients diagnosed with nontractable epilepsy who were implanted with entorhinal cortical electrodes performing virtual navigation tasks to memorized locations enabled us to investigate associations between grid-like patterns and environment. Here, we report that the activity of human entorhinal cortical neurons exhibits adaptive scaling in grid period, grid orientation, and rotational symmetry in close association with changes in environment size, shape, and visual cues, suggesting scale invariance of the frequency, rather than the wavelength, of spatially periodic activity. Our results demonstrate that neurons in the human EC represent space with an enhanced flexibility relative to neurons in rodents because they are endowed with adaptive scalability and context dependency.

Ten Years of Grid Cells

The medial entorhinal cortex (MEC) creates a neural representation of space through a set of functionally dedicated cell types: grid cells, border cells, head direction cells, and speed cells. Grid cells, the most abundant functional cell type in the MEC, have hexagonally arranged firing fields that tile the surface of the environment. These cells were discovered only in 2005, but after 10 years of investigation, we are beginning to understand how they are organized in the MEC network, how their periodic firing fields might be generated, how they are shaped by properties of the environment, and how they interact with the rest of the MEC network. The aim of this review is to summarize what we know about grid cells and point out where our knowledge is still incomplete.

The Art of Grid Fields: Geometry of Neuronal Time

The discovery of grid cells in the entorhinal cortex has both elucidated our understanding of spatial representations in the brain, and germinated a large number of theoretical models regarding the mechanisms of these cells' striking spatial firing characteristics. These models cross multiple neurobiological levels that include intrinsic membrane resonance, dendritic integration, after hyperpolarization characteristics and attractor dynamics. Despite the breadth of the models, to our knowledge, parallels can be drawn between grid fields and other temporal dynamics observed in nature, much of which was described by Art Winfree and colleagues long before the initial description of grid fields. Using theoretical and mathematical investigations of oscillators, in a wide array of mediums far from the neurobiology of grid cells, Art Winfree has provided a substantial amount of research with significant and profound similarities. These theories provide specific inferences into the biological mechanisms and extraordinary resemblances across phenomenon. Therefore, this manuscript provides a novel interpretation on the phenomenon of grid fields, from the perspective of coupled oscillators, postulating that grid fields are the spatial representation of phase resetting curves in the brain. In contrast to prior models of gird cells, the current manuscript provides a sketch by which a small network of neurons, each with oscillatory components can operate to form grid cells, perhaps providing a unique hybrid between the competing attractor neural network and oscillatory interference models. The intention of this new interpretation of the data is to encourage novel testable hypotheses.