Spatial coding and attractor dynamics of grid cells in the entorhinal cortex

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal is to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software (version 1.0) is released as open source to enable broad community reuse and encourage novel applications.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal was to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software is released as open source to enable broad community reuse and encourage novel applications.

Sources of richness and ineffability for phenomenally conscious states

Conscious states-state that there is something it is like to be in-seem both rich or full of detail and ineffable or hard to fully describe or recall. The problem of ineffability, in particular, is a longstanding issue in philosophy that partly motivates the explanatory gap: the belief that consciousness cannot be reduced to underlying physical processes. Here, we provide an information theoretic dynamical systems perspective on the richness and ineffability of consciousness. In our framework, the richness of conscious experience corresponds to the amount of information in a conscious state and ineffability corresponds to the amount of information lost at different stages of processing. We describe how attractor dynamics in working memory would induce impoverished recollections of our original experiences, how the discrete symbolic nature of language is insufficient for describing the rich and high-dimensional structure of experiences, and how similarity in the cognitive function of two individuals relates to improved communicability of their experiences to each other. While our model may not settle all questions relating to the explanatory gap, it makes progress toward a fully physicalist explanation of the richness and ineffability of conscious experience-two important aspects that seem to be part of what makes qualitative character so puzzling.

Grid cells: the missing link in understanding Parkinson's disease?

The mechanisms underlying Parkinson's disease (PD) are complex and not fully understood, and the box-and-arrow model among other current models present significant challenges. This paper explores the potential role of the allocentric brain and especially its grid cells in several PD motor symptoms, including bradykinesia, kinesia paradoxa, freezing of gait, the bottleneck phenomenon, and their dependency on cueing. It is argued that central hubs, like the locus coeruleus and the pedunculopontine nucleus, often narrowly interpreted in the context of PD, play an equally important role in governing the allocentric brain as the basal ganglia. Consequently, the motor and secondary motor (e.g., spatially related) symptoms of PD linked with dopamine depletion may be more closely tied to erroneous computation by grid cells than to the basal ganglia alone. Because grid cells and their associated central hubs introduce both spatial and temporal information to the brain influencing velocity perception they may cause bradykinesia or hyperkinesia as well. In summary, PD motor symptoms may primarily be an allocentric disturbance resulting from virtual faulty computation by grid cells revealed by dopamine depletion in PD.

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.

Grid-cell modules remain coordinated when neural activity is dissociated from external sensory cues

The representation of an animal’s position in the medial entorhinal cortex (MEC) is distributed across several modules of grid cells, each characterized by a distinct spatial scale. The population activity within each module is tightly coordinated and preserved across environments and behavioral states. Little is known, however, about the coordination of activity patterns across modules. We analyzed the joint activity patterns of hundreds of grid cells simultaneously recorded in animals that were foraging either in the light, when sensory cues could stabilize the representation, or in darkness, when such stabilization was disrupted. We found that the states of different modules are tightly coordinated, even in darkness, when the internal representation of position within the MEC deviates substantially from the true position of the animal. These findings suggest that internal brain mechanisms dynamically coordinate the representation of position in different modules, ensuring that they jointly encode a coherent and smooth trajectory.

•

Hundreds of grid cells were recorded simultaneously from multiple grid modules

•

Coordination between grid modules was assessed in rats that foraged in darkness

•

Coordination persists despite relative drift of the represented versus true position

•

This suggests that internal network mechanisms maintain inter-module coordination

The grid code for ordered experience

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

Toward a Unified Framework for Cognitive Maps

In this study, we integrated neural encoding and decoding into a unified framework for spatial information processing in the brain. Specifically, the neural representations of self-location in the hippocampus (HPC) and entorhinal cortex (EC) play crucial roles in spatial navigation. Intriguingly, these neural representations in these neighboring brain areas show stark differences. Whereas the place cells in the HPC fire as a unimodal function of spatial location, the grid cells in the EC show periodic tuning curves with different periods for different subpopulations (called modules). By combining an encoding model for this modular neural representation and a realistic decoding model based on belief propagation, we investigated the manner in which self-location is encoded by neurons in the EC and then decoded by downstream neurons in the HPC. Through the results of numerical simulations, we first show the positive synergy effects of the modular structure in the EC. The modular structure introduces more coupling between heterogeneous modules with different periodicities, which provides increased error-correcting capabilities. This is also demonstrated through a comparison of the beliefs produced for decoding two- and four-module codes. Whereas the former resulted in a complete decoding failure, the latter correctly recovered the self-location even from the same inputs. Further analysis of belief propagation during decoding revealed complex dynamics in information updates due to interactions among multiple modules having diverse scales. Therefore, the proposed unified framework allows one to investigate the overall flow of spatial information, closing the loop of encoding and decoding self-location in the brain.

A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

The representation of position in the mammalian brain is distributed across multiple neural populations. Grid cell modules in the medial entorhinal cortex (MEC) express activity patterns that span a low-dimensional manifold which remains stable across different environments. In contrast, the activity patterns of hippocampal place cells span distinct low-dimensional manifolds in different environments. It is unknown how these multiple representations of position are coordinated. Here, we develop a theory of joint attractor dynamics in the hippocampus and the MEC. We show that the system exhibits a coordinated, joint representation of position across multiple environments, consistent with global remapping in place cells and grid cells. In addition, our model accounts for recent experimental observations that lack a mechanistic explanation: variability in the firing rate of single grid cells across firing fields, and artificial remapping of place cells under depolarization, but not under hyperpolarization, of layer II stellate cells of the MEC.

Velocity coupling of grid cell modules enables stable embedding of a low dimensional variable in a high dimensional neural attractor

Grid cells in the medial entorhinal cortex (MEC) encode position using a distributed representation across multiple neural populations (modules), each possessing a distinct spatial scale. The modular structure of the representation confers the grid cell neural code with large capacity. Yet, the modularity poses significant challenges for the neural circuitry that maintains the representation, and updates it based on self motion. Small incompatible drifts in different modules, driven by noise, can rapidly lead to large, abrupt shifts in the represented position, resulting in catastrophic readout errors. Here, we propose a theoretical model of coupled modules. The coupling suppresses incompatible drifts, allowing for a stable embedding of a two-dimensional variable (position) in a higher dimensional neural attractor, while preserving the large capacity. We propose that coupling of this type may be implemented by recurrent synaptic connectivity within the MEC with a relatively simple and biologically plausible structure.

Partial coherence and frustration in self-organizing spherical grids

Nearby grid cells have been observed to express a remarkable degree of long-range order, which is often idealized as extending potentially to infinity. Yet their strict periodic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.

Stability of working memory in continuous attractor networks under the control of short-term plasticity

Continuous attractor models of working-memory store continuous-valued information in continuous state-spaces, but are sensitive to noise processes that degrade memory retention. Short-term synaptic plasticity of recurrent synapses has previously been shown to affect continuous attractor systems: short-term facilitation can stabilize memory retention, while short-term depression possibly increases continuous attractor volatility. Here, we present a comprehensive description of the combined effect of both short-term facilitation and depression on noise-induced memory degradation in one-dimensional continuous attractor models. Our theoretical description, applicable to rate models as well as spiking networks close to a stationary state, accurately describes the slow dynamics of stored memory positions as a combination of two processes: (i) diffusion due to variability caused by spikes; and (ii) drift due to random connectivity and neuronal heterogeneity. We find that facilitation decreases both diffusion and directed drifts, while short-term depression tends to increase both. Using mutual information, we evaluate the combined impact of short-term facilitation and depression on the ability of networks to retain stable working memory. Finally, our theory predicts the sensitivity of continuous working memory to distractor inputs and provides conditions for stability of memory.

The ability to transiently memorize positions in the visual field is crucial for behavior. Models and experiments have shown that such memories can be maintained in networks of cortical neurons with a continuum of possible activity states, that reflects the continuum of positions in the environment. However, the accuracy of positions stored in such networks will degrade over time due to the noisiness of neuronal signaling and imperfections of the biological substrate. Previous work in simplified models has shown that synaptic short-term plasticity could stabilize this degradation by dynamically up- or down-regulating the strength of synaptic connections, thereby “pinning down” memorized positions. Here, we present a general theory that accurately predicts the extent of this “pinning down” by short-term plasticity in a broad class of biologically plausible network models, thereby untangling the interplay of varying biological sources of noise with short-term plasticity. Importantly, our work provides a novel theoretical link from the microscopic substrate of working memory—neurons and synaptic connections—to observable behavioral correlates, for example the susceptibility to distracting stimuli.

Social behaviour shapes hypothalamic neural ensemble representations of conspecific sex

All animals possess a repertoire of innate (or instinctive^1,2) behaviors, which can be performed without training. Whether such behaviors are mediated by anatomically distinct and/or genetically specified neural pathways remains a matter of debate^3-5. Here we report that hypothalamic neural ensemble representations underlying innate social behaviors are shaped by social experience. Estrogen receptor 1-expressing (Esr1⁺) neurons in the ventrolateral subdivision of the ventromedial hypothalamus (VMHvl) control mating and fighting in rodents^6-8. We used microendoscopy⁹ to image VMHvl Esr1⁺ neuronal activity in male mice engaged in these social behaviours. In sexually and socially experienced adult males, divergent and characteristic neural ensembles represented male vs. female conspecifics. But surprisingly, in inexperienced adult males, male and female intruders activated overlapping neuronal populations. Sex-specific ensembles gradually separated as the mice acquired social and sexual experience. In mice permitted to investigate but not mount or attack conspecifics, ensemble divergence did not occur. However, 30 min of sexual experience with a female was sufficient to promote both male vs. female ensemble separation and attack, measured 24 hr later. These observations uncover an unexpected social experience-dependent component to the formation of hypothalamic neural assemblies controlling innate social behaviors. More generally, they reveal plasticity and dynamic coding in an evolutionarily ancient deep subcortical structure that is traditionally viewed as a “hard-wired” system.

Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and conceptual spaces

Across the nervous system, neurons often encode circular stimuli using tuning curves that are not sine or cosine functions, but that belong to the richer class of von Mises functions, which are periodic variants of Gaussians. For a population of neurons encoding a single circular variable with such canonical tuning curves, computing a simple population vector is the optimal read-out of the most likely stimulus. We argue that the advantages of population vector read-outs are so compelling that even the neural representation of the outside world's flat Euclidean geometry is curled up into a torus (a circle times a circle), creating the hexagonal activity patterns of mammalian grid cells. Here, the circular scale is not set a priori, so the nervous system can use multiple scales and gain fields to overcome the ambiguity inherent in periodic representations of linear variables. We review the experimental evidence for this framework and discuss its testable predictions and generalizations to more abstract grid-like neural representations.

Spatial Cognition: Grid Cells Harbour Three Complementary Positional Codes

The firing fields of mammalian grid cells, which map an animal's environment, lie on hexagonal lattices. Three new studies report significant field-to-field differences in the firing rates, a finding with far-reaching consequences for how grid fields form and encode spatial information.

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.

Local and Distant Input Controlling Excitation in Layer II of the Medial Entorhinal Cortex

Layer II (LII) of the medial entorhinal cortex (MEC) comprises grid cells that support spatial navigation. The firing pattern of grid cells might be explained by attractor dynamics in a network, which requires either direct excitatory connectivity between phase-specific grid cells or indirect coupling via interneurons. However, knowledge regarding local networks that support in vivo activity is incomplete. Here we identified essential components of LII networks in the MEC. We distinguished four types of excitatory neurons that exhibit cell-type-specific local excitatory and inhibitory connectivity. Furthermore, we found that LII neurons contribute to the excitation of contralateral neurons in the corresponding layer. Finally, we demonstrated that the medial septum controls excitation in the MEC via two subpopulations of long-range GABAergic neurons that target distinct interneurons in LII, thereby disinhibiting local circuits. We thus identified local connections that could support attractor dynamics and external inputs that likely govern excitation in LII.

•

LII MEC excitatory neurons can be classified into four cell types

•

The four cell types exhibit specific local excitatory and inhibitory connectivity

•

LII neurons contribute to the excitation of contralateral LII neurons

•

Distinct septal GABAergic neurons exhibit cell-type-specific inhibition in LII MEC

Connecting multiple spatial scales to decode the population activity of grid cells

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

Exposure to extremely low frequency electromagnetic fields alters the calcium dynamics of cultured entorhinal cortex neurons

Previous studies have revealed that extremely low frequency electromagnetic field (ELF-EMF) exposure affects neuronal dendritic spine density and NMDAR and AMPAR subunit expressions in the entorhinal cortex (EC). Although calcium signaling has a critical role in control of EC neuronal functions, however, it is still unclear whether the ELF-EMF exposure affects the EC neuronal calcium homeostasis. In the present study, using whole-cell recording and calcium imaging, we record the whole-cell inward currents that contain the voltage-gated calcium currents and show that ELF-EMF (50Hz, 1mT or 3mT, lasting 24h) exposure does not influence these currents. Next, we specifically isolate the high-voltage activated (HVA) and low-voltage activated (LVA) calcium channels-induced currents. Similarly, the activation and inactivation characteristics of these membrane calcium channels are also not influenced by ELF-EMF. Importantly, ELF-EMF exposure reduces the maximum amplitude of the high-K(+)-evoked calcium elevation in EC neurons, which is abolished by thapsigargin, a Ca(2+) ATPase inhibitor, to empty the intracellular calcium stores of EC neurons. Together, these findings indicate that ELF-EMF exposure specifically influences the intracellular calcium dynamics of cultural EC neurons via a calcium channel-independent mechanism.

Computational neuroscience: beyond the local circuit

Computational neuroscience has focused largely on the dynamics and function of local circuits of neuronal populations dedicated to a common task, such as processing a common sensory input, storing its features in working memory, choosing between a set of options dictated by controlled experimental settings or generating the appropriate actions. Most of current circuit models suggest mechanisms for computations that can be captured by networks of simplified neurons connected via simple synaptic weights. In this article I review the progress of this approach and its limitations. It is argued that new experimental techniques will yield data that might challenge the present paradigms in that they will (1) demonstrate the computational importance of microscopic structural and physiological complexity and specificity; (2) highlight the importance of models of large brain structures engaged in a variety of tasks; and (3) reveal the necessity of coupling the neuronal networks to chemical and environmental variables.