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.

The firing patterns of grid cells in medial entorhinal cortex (mEC) and associated brain areas form triangular arrays that tessellate the environment and maintain constant spatial offsets to each other between environments. These cells are thought to provide an efficient metric for navigation in large-scale space. However, an accurate and universal metric requires grid cell firing patterns to uniformly cover the space to be navigated, in contrast to recent demonstrations that environmental features such as boundaries can distort and fragment grid patterns. To establish whether grid firing is determined by local environmental cues, or provides a coherent global representation, we recorded mEC grid cells in rats foraging in an environment containing two perceptually identical compartments connected via a corridor. During initial exposures to the multicompartment environment, grid firing patterns were dominated by local environmental cues, replicating between the two compartments. However, with prolonged experience, grid cell firing patterns formed a single, continuous representation that spanned both compartments. Thus, we provide the first evidence that in a complex environment, grid cell firing can form the coherent global pattern necessary for them to act as a metric capable of supporting large-scale spatial navigation.

The representation of self-location by grid cells has variously been described as “densely packed” or “hexagonal”; leading to hypotheses about the role of a grid cell network in providing a metric for space. However, recently, it was shown that exposure to environmental novelty provokes a temporary increase in grid scale, which attenuates with increasing familiarity. This differs from evidence that grids are anchored to sensory cues, and can be rotated or stretched by changes to sensory cues, and suggests that grid cells do not simply provide a fixed metric for space that becomes attached to environmental cues. The exact neural mechanisms driving grid scale expansion and its functional role are currently unknown. However, it has been hypothesised that grid scale varies inversely with the precision with which the animal’s self-location can be determined (spatial uncertainty), so as to encode location more accurately. Thus grid scale would be expected to increase in situations with few spatial cues or unknown configurations of cues, such as in a novel environment, compared to situations in which multiple cues were accessible. To test this hypothesis, we recorded medial entorhinal grid cells while rats foraged in two types of environment: one rich in local cues and the other lacking any such cues. It was hypothesised that grid scale would be smaller in the cue rich environment, reflecting higher certainty in the representation of self-location, similar to that observed in familiar environments. We recorded cells in both environments from their first experience of it and throughout the familiarisation process. We found that grid patterns had a smaller scale in the cue rich environment, supporting the hypothesis, and were also more regular. This confirms that the grid cells do not simply encode a fixed metric for space, rather the encoding is sensitive to additional factors such as environmental novelty and the availability of cues.

Place and grid cells in the rodent hippocampal formation tend to fire spikes at successively earlier phases relative to the local field potential theta rhythm as the animal runs through the cell's firing field on a linear track. However, this 'phase precession' effect is less well characterized during foraging in two-dimensional open field environments. Here, we mapped runs through the firing fields onto a unit circle to pool data from multiple runs. We asked which of seven behavioural and physiological variables show the best circular-linear correlation with the theta phase of spikes from place cells in hippocampal area CA1 and from grid cells from superficial layers of medial entorhinal cortex. The best correlate was the distance to the firing field peak projected onto the animal's current running direction. This was significantly stronger than other correlates, such as instantaneous firing rate and time-in-field, but similar in strength to correlates with other measures of distance travelled through the firing field. Phase precession was stronger in place cells than grid cells overall, and robust phase precession was seen in traversals through firing field peripheries (although somewhat less than in traversals through the centre), consistent with phase coding of displacement along the current direction. This type of phase coding, of place field distance ahead of or behind the animal, may be useful for allowing calculation of goal directions during navigation.

Cells in mammalian primary visual cortex respond preferentially to bars of lightness or darkness on the retina. For a long time it has been known that the extent of this sensitivity does not depend on the contrast of the stimulus. It has recently been shown that this invariance also exists in the shape of the time-averaged population response. Here we examine whether invariance of the population holds over much shorter time periods, and tentatively conclude that it does.

It is relatively common for the brain of perinatal infants to be exposed to a period of reduced oxygen (hypoxia) and reduced blood flow (ischemia). Left untreated, these episodes tend to cause permanent damage to the brain. In order to understand how this damage arises and whether it is preventable, an extensive computational model has been developed that attempts to accurately capture the full metabolic complexity of the infant brain. This complexity encompasses everything from haemodynamics, to calcium channels in vascular muscle, to oxidative phosphorylation in the mitochondria of neurons. Model parameters are set using data from in vivo and in vitro experiments, as well as using a range of more ad hoc measures such as steady-state analysis. In the current model there is no distinction between astrocytes and neurons, i.e. the cell in the model is a rough average of the two. However there is plenty of evidence that astrocytes and neurons have quite different metabolic properties and interact in non-trivial ways. In this work we examine a separate model, designed for looking at the metabolic interactions of astrocytes and neurons, and examine whether any of its dynamics should be incorporated into the hypoxia model.

If identified at an early stage, cancer of the esophagus can be removed non-invasively using an endoscope. However, the site of removed tissue rarely recovers completely, and is commonly replaced by a large volume of scar tissue, in some cases causing a significant narrowing of the esophagus. To prevent such post-operative problems it has been proposed that healthy replacement tissue be applied to the site of the cancer, having been grown in vitro from the patient's own cells. In this work we consider one method for improving the adhesion of the new cells to the target site. The method involves seeding the in vitro cells with magnetic particles, and subsequently applying a magnetic force to them using an externally administered permanent magnet, applied for a few minutes during the grafting procedure.

Following a week-long course at the Marine Biology Assosiation's laboratory in Plymouth, MRes students are required to produce a poster relating to something they have learnt. Producing and presenting the poster gives students a chance to practice important 'transferable' skills. I chose to make a poster on krill and their role in the marine carbon system.

Despite impressive advances over the last several decades, to a large extent the human brain remains something of a black-box. This state of affairs is easily understood given that the `machine inside the box' consists of a network of approximately 10¹¹ nodes, each of which transmits electrical signals in a highly non-linear and ever changing manner. Investigation of individual cell types has been relatively successful in primary sensorary areas and hippocompus, but there is yet to be any signiffcant progress in understanding the dynamics of small populations of cells. Appropriate grouping of these small populations results in a brain divided into approximately 1000 regions. These regions can then be further aggregated to produce a labeled map of the brain at the mesoscopic scale where there are about 66 distinct regions. EEG, MEG and fMRI make it possible to record brain activity at this coarse level of network description. In this work we model the 66 regions as a network of weakly coupled oscillators, i.e as a Kuramoto model, and compare model simulations to MEG data collected at resting state.