Daniel Bush

What do grid cells contribute to place cell firing

Highlights • It is commonly assumed that grid cell inputs generate hippocampal place fields, but recent empirical evidence brings this assumption into doubt.• We suggest that place fields are primarily determined by environmental sensory inputs.• Grid cells provide a complementary path integration input and large-scale spatial metric.• Place and grid cell representations interact to support accurate coding of large-scale space.

A Hybrid Oscillatory Interference/Continuous Attractor Network Model of Grid Cell Firing

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account for experimental data. The oscillatory interference model proposes that the grid pattern is formed from linear interference patterns or “periodic bands” in which velocity-controlled oscillators integrate self-motion to code displacement along preferred directions. However, it also allows the use of symmetric recurrent connectivity between grid cells to provide relative stability and continuous attractor dynamics. Here, we present simulations of this type of hybrid model, demonstrate that it generates intracellular membrane potential profiles that closely match those observed in vivo, addresses several criticisms aimed at pure oscillatory interference and continuous attractor models, and provides testable predictions for future empirical studies.

Using Grid Cells for Navigation

Summary Mammals are able to navigate to hidden goal locations by direct routes that may traverse previously unvisited terrain. Empirical evidence suggests that this “vector navigation” relies on an internal representation of space provided by the hippocampal formation. The periodic spatial firing patterns of grid cells in the hippocampal formation offer a compact combinatorial code for location within large-scale space. Here, we consider the computational problem of how to determine the vector between start and goal locations encoded by the firing of grid cells when this vector may be much longer than the largest grid scale. First, we present an algorithmic solution to the problem, inspired by the Fourier shift theorem. Second, we describe several potential neural network implementations of this solution that combine efficiency of search and biological plausibility. Finally, we discuss the empirical predictions of these implementations and their relationship to the anatomy and electrophysiology of the hippocampal formation.

Medial prefrontal theta phase coupling during spatial memory retrieval

Memory retrieval is believed to involve a disparate network of areas, including medial prefrontal and medial temporal cortices, but the mechanisms underlying their coordination remain elusive. One suggestion is that oscillatory coherence mediates inter‐regional communication, implicating theta phase and theta‐gamma phase‐amplitude coupling in mnemonic function across species. To examine this hypothesis, we used non‐invasive whole‐head magnetoencephalography (MEG) as participants retrieved the location of objects encountered within a virtual environment. We demonstrate that, when participants are cued with the image of an object whose location they must subsequently navigate to, there is a significant increase in 4–8 Hz theta power in medial prefrontal cortex (mPFC), and the phase of this oscillation is coupled both with ongoing theta phase in the medial temporal lobe (MTL) and perceptually induced 65–85 Hz gamma amplitude in medial parietal cortex. These results suggest that theta phase coupling between mPFC and MTL and theta‐gamma phase‐amplitude coupling between mPFC and neocortical regions may play a role in human spatial memory retrieval.

Grid-like Processing of Imagined Navigation

Summary Grid cells in the entorhinal cortex (EC) of rodents [1] and humans [2] fire in a hexagonally distributed spatially periodic manner. In concert with other spatial cells in the medial temporal lobe (MTL) [3, 4, 5, 6], they provide a representation of our location within an environment [7, 8] and are specifically thought to allow the represented location to be updated by self-motion [9]. Grid-like signals have been seen throughout the autobiographical memory system [10], suggesting a much more general role in memory [11, 12]. Grid cells may allow us to move our viewpoint in imagination [13], a useful function for goal-directed navigation and planning [12, 14, 15, 16], and episodic future thinking more generally [17, 18]. We used fMRI to provide evidence for similar grid-like signals in human entorhinal cortex during both virtual navigation and imagined navigation of the same paths. We show that this signal is present in periods of active navigation and imagination, with a similar orientation in both and with the specifically 6-fold rotational symmetry characteristic of grid cell firing. We therefore provide the first evidence suggesting that grid cells are utilized during movement of viewpoint within imagery, potentially underpinning our more general ability to mentally traverse possible routes in the service of planning and episodic future thinking.

Recruitment of resting vesicles into recycling pools supports NMDA-receptor dependent synaptic potentiation in cultured hippocampal neurons

•  Presynaptic terminals in hippocampal neurons are characterized by two functionally defined vesicle populations: a recycling pool, which supports activity‐evoked neurotransmission, and a resting pool. •  Between individual synapses, the relative proportions of these two pools are highly variable, suggesting that this parameter might be specifically regulated to support changes in synaptic efficacy. •  Using fluorescence imaging and correlative ultrastructural approaches we show here that a form of synaptic potentiation dependent on N‐methyl‐d‐aspartic acid (NMDA) receptor activity can lead to a rapid and sustained expansion of the recycling fraction at the expense of the resting pool. •  This recruitment of vesicles depends on nitric oxide signalling and calcineurin activity, and is accompanied by an increase in synaptic release probability. •  We suggest that vesicle exchange between these pools provides a rapid mechanism to support adjustments in synaptic strength associated with a form of Hebbian plasticity.

Models of grid cells and theta oscillations

Arising from M. M.Yartsev, M. P. Witter & N. Ulanovsky 479, 103–107 (2011)10.1038/nature10583Grid cells recorded in the medial entorhinal cortex (MEC) of freely moving rodents show a markedly regular spatial firing pattern whose underlying mechanism has been the subject of intense interest. Yartsev et al. report that the firing of grid cells in crawling bats does not show theta rhythmicity “causally disproving a major class of computational models” of grid cell firing that rely on oscillatory interference. However, their data may be consistent with these models, with the apparent lack of theta rhythmicity reflecting slow movement speeds and low firing rates. Thus, the conclusion of Yartsev et al. is not supported by their data.

Dual Coding with STDP in a Spiking Recurrent Neural Network Model of the Hippocampus

The firing rate of single neurons in the mammalian hippocampus has been demonstrated to encode for a range of spatial and non-spatial stimuli. It has also been demonstrated that phase of firing, with respect to the theta oscillation that dominates the hippocampal EEG during stereotype learning behaviour, correlates with an animals spatial location. These findings have led to the hypothesis that the hippocampus operates using a dual (rate and temporal) coding system. To investigate the phenomenon of dual coding in the hippocampus, we examine a spiking recurrent network model with theta coded neural dynamics and an STDP rule that mediates rate-coded Hebbian learning when pre- and post-synaptic firing is stochastic. We demonstrate that this plasticity rule can generate both symmetric and asymmetric connections between neurons that fire at concurrent or successive theta phase, respectively, and subsequently produce both pattern completion and sequence prediction from partial cues. This unifies previously disparate auto- and hetero-associative network models of hippocampal function and provides them with a firmer basis in modern neurobiology. Furthermore, the encoding and reactivation of activity in mutually exciting Hebbian cell assemblies demonstrated here is believed to represent a fundamental mechanism of cognitive processing in the brain.

Reconciling the stdp and bcm models of synaptic plasticity in a spiking recurrent neural network

Rate-coded Hebbian learning, as characterized by the BCM formulation, is an established computational model of synaptic plasticity. Recently it has been demonstrated that changes in the strength of synapses in vivo can also depend explicitly on the relative timing of pre- and postsynaptic firing. Computational modeling of this spike-timing-dependent plasticity (STDP) has demonstrated that it can provide inherent stability or competition based on local synaptic variables. However, it has also been demonstrated that these properties rely on synaptic weights being either depressed or unchanged by an increase in mean stochastic firing rates, which directly contradicts empirical data. Several analytical studies have addressed this apparent dichotomy and identified conditions under which distinct and disparate STDP rules can be reconciled with rate-coded Hebbian learning. The aim of this research is to verify, unify, and expand on these previous findings by manipulating each element of a standard computational STDP model in turn. This allows us to identify the conditions under which this plasticity rule can replicate experimental data obtained using both rate and temporal stimulation protocols in a spiking recurrent neural network. Our results describe how the relative scale of mean synaptic weights and their dependence on stochastic pre- or postsynaptic firing rates can be manipulated by adjusting the exact profile of the asymmetric learning window and temporal restrictions on spike pair interactions respectively. These findings imply that previously disparate models of rate-coded autoassociative learning and temporally coded heteroassociative learning, mediated by symmetric and asymmetric connections respectively, can be implemented in a single network using a single plasticity rule. However, we also demonstrate that forms of STDP that can be reconciled with rate-coded Hebbian learning do not generate inherent synaptic competition, and thus some additional mechanism is required to guarantee long-term input-output selectivity.

Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.